Download Constraining the initial properties of Terrestrial Gamma

Constraining the initial properties of
Terrestrial Gamma-ray Flashes
Ragnhild Schrøder Nisi
Dissertation for the degree of Philosophiae Doctor (PhD)
Department of Physics and Technology
University of Bergen
May 2014
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Preface
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Preface
Contents
Preface
i
List of Figures
v
List of papers
ix
Acknowledgements
xi
1 Introduction
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2 Observations
2.1 Satellite observations of TGFs . . . . . . . . . . . . . . . . . . . . .
2.1.1 The Burst and Transient Source Experiment . . . . . . . . . .
2.1.2 The Reuven Ramaty High Energy Solar Spectroscopic Imager
2.1.3 Astrorivelatore Gamma a Immagini Leggero . . . . . . . . .
2.1.4 Fermi Gamma-ray Space Telescope . . . . . . . . . . . . . .
2.2 Airborne and ground observations of TGFs . . . . . . . . . . . . . .
2.2.1 Airborne Detector for Energetic Lightning Emissions . . . . .
2.2.2 Detection from ground . . . . . . . . . . . . . . . . . . . . .
2.2.3 Radio waves from TGFs . . . . . . . . . . . . . . . . . . . .
2.2.4 Observability of TGFs by aircraft and balloon . . . . . . . . .
2.3 Observations of lightning . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Low Frequencies . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 High Frequency and Very High Frequency . . . . . . . . . . .
2.3.3 Satellite measurements . . . . . . . . . . . . . . . . . . . . .
2.4 X-rays from lightning and laboratory sparks . . . . . . . . . . . . . .
2.4.1 X-rays from lightning . . . . . . . . . . . . . . . . . . . . .
2.4.2 X-rays from laboratory sparks . . . . . . . . . . . . . . . . .
3 Theories of production
3.1 Relativistic Runaway Electron Avalanche
3.2 Thunderstorms and lightning . . . . . . .
3.2.1 Initiation of lightning . . . . . . .
3.2.2 Streamer and leader process . . .
3.3 The Thermal runaway theory . . . . . . .
3.4 Feedback . . . . . . . . . . . . . . . . .
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4 Modeling of TGFs
4.1 Photon transport in air . . . . . . . . . . . .
4.2 The bremsstrahlung process . . . . . . . . .
4.2.1 The Born approximation . . . . . . .
4.2.2 The Sommerfelt-Maue wave function
4.2.3 Use in models . . . . . . . . . . . . .
CONTENTS
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5 Source properties of TGFs
5.1 Space and time distributions . . . . . . . . . . . . . . . . . .
5.1.1 Geographical distribution . . . . . . . . . . . . . . . .
5.1.2 Distance from satellite nadir . . . . . . . . . . . . . .
5.1.3 Annual and diurnal distributions . . . . . . . . . . . .
5.1.4 Duration of TGFs . . . . . . . . . . . . . . . . . . . .
5.1.5 Timing of TGFs . . . . . . . . . . . . . . . . . . . .
5.2 Number of TGFs . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 TGF/lightning . . . . . . . . . . . . . . . . . . . . .
5.2.2 Total global number of TGFs . . . . . . . . . . . . . .
5.2.3 x-ray/spark . . . . . . . . . . . . . . . . . . . . . . .
5.3 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Altitude distribution . . . . . . . . . . . . . . . . . . . . . . .
5.5 Emission angles of TGF photons . . . . . . . . . . . . . . . .
5.6 Number of initial photons . . . . . . . . . . . . . . . . . . . .
5.7 Number of electrons . . . . . . . . . . . . . . . . . . . . . .
5.8 How the determination of source properties affects the theories
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6 Introduction to the papers
47
Bibliography
49
Acronyms
61
Nomenclature
63
Scientific results
67
6.1 The true fluence distribution of terrestrial gamma flashes at satellite
altitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.2 How simulated fluence of photons from terrestrial gamma ray flashes
at aircraft and balloon altitudes depends on initial parameters . . . . . . 79
6.3 An altitude and distance correction to the initial fluence distribution of
TGFs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
List of Figures
2.1
2.2
2.3
2.4
An illustration of the two main detector responses to photons hitting
the detector when the detector is dead. The top panel shows the time
of the incoming photons, the middle panel shows the response of a
nonparalyzable detector, and the lower panel shows the response of a
paralyzable detector. The red lines mark the photons that are registrered
by the detector. The paralyzable detector start a new dead time for
photons hitting the detector within the deadtime of a previous photon.
This can make the detector dead for long periods of time if new photons
are arriving too short after one another. . . . . . . . . . . . . . . . . . .
4
An illustration of the number of measured counts vs true counts in a
paralyzable and a nonparalyzable detector. The ideal detector would
measure the true number of photons, but the actual detectors measure
less than the actual number when the number of photons are more than
a few tens in this example. Note that for the paralyzable detector, the
measured number of photons can relate to two different numbers of true
photons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
The dead time of RHESSI as found from Monte Carlo simulations of a
TGF detected on May 2. 2005. The duration of the TGF was 362 µ s
and the TGF consisted of 30 measured photons. The gray error bars are
calculated from repeating the simulation 100 times. The figure shows
that the RHESSI instrumentation is mostly able to detect all photons up
to around 15 photons per TGF. For higher fluxes of photons RHESSI
will be affected by the dead time, and not all photons detected. For this
TGF with 30 measured photons, the true number was probably between
35 and 45 photons. This figure is adapted from Østgaard et al. [2012]
(Paper 1 of this thesis). . . . . . . . . . . . . . . . . . . . . . . . . . .
6
X-rays from a triggered lightning reported by Dwyer et al. [2004]. The
red diamonds are the recorded data, the black curve is the detector response. This shows several µ s-duration bursts of energetic radiation
just before the lightning return stroke (t=0). . . . . . . . . . . . . . . . 10
vi
LIST OF FIGURES
2.5
Photos of a positive polarity spark using a camera with very high shutter
speed at different points during a spark development. The panel at
the bottom show the times of the photos, the voltage across the gap
(U), the current on the high voltage electrode (IHV ), the current of the
ground electrode (IGND ) and the signal from x-rays as detected by a
LaBr-detector. The two arrows in the first photo mark the electrode tip
(lower arrow) and the streamers created on the top of the electrode disk.
The photos show that the x-rays are created just before the streamers
from the two electrodes connect. . . . . . . . . . . . . . . . . . . . . . 12
3.1
Friction force for electrons in air at standard surface pressure. If an
electron with energy of εth experience an electric field greater than or
equal to E it will accelerate to relativistic energy. Eb and a seed electron of ε ≈ 1 MeV is the weakest electric field that can give a runaway
electron. The other electric fields in the figure is explained in the text.
Figure adapted from Dwyer et al. [2012a] . . . . . . . . . . . . . . .
Illustration of the charge structure of thunderstorms adapted from
Stolzenburg et al. [1998]. The cloud has a main negative at around 25 °C and a main positive above that. In addition the screening charges
create a basic quadrapole charge structure in the updraft region. In the
downpour region more layers are present. . . . . . . . . . . . . . . .
Measured electric field (solid curve) and integrated voltage (dashed)
for a balloon sounding on August 1. 1984. Approximate altitude and
polarity of the charge regions of the cloud are shown at the right. This
was inferred using a one-dimensional approximation to Gauss law. The
figure is adapted from Marshall and Stolzenburg [2001]. . . . . . . .
A simulation of the runaway breakdown process from Dwyer [2005]. A
positive region is placed on top of the figure, and a negative on the bottom. If this ambient field is larger than Eb that is the limit for runaway
breakdown, some electrons will start accelerating towards the positive
region. These accelerating charges will create ionization and hence
increase the field in a small region. The field will lead to more acceleration and more ionization and hence the process will escalate. In this
figure the black arrows depicts the trajectories of the runaway electrons
and the electric field strengths at the 1 atmosphere equivalent are shown
in colors. In the white region where the electric field is around 1 MV/m
a streamer might form if a hydrometeor is present. . . . . . . . . . . .
A schematic drawing of the propagation of positive (a) and negative
(b) streamers. In front of both streamers, small avalanches of electrons form. For the positive streamer, these avalanches will be attracted
towards the streamer tip and the streamer will expand in an almost constant way. For the negative streamer, the avalanches will be repelled
from the streamer tip. When the avalanches has created enough ionization in front of the streamer tip, the streamer will jump to this ionized
region and thus expand in a step-wise manner. Image credit: Alexander
Skeltved . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
3.3
3.4
3.5
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LIST OF FIGURES
3.6
3.7
3.8
4.1
4.2
5.1
5.2
5.3
5.4
vii
An illustration of the tip of the streamer, depicting how the surface
charge create a region of strong electric field at the tip of the streamer.
This field can be large enough to accelerate low energy electrons to keV
energies. Image credit: Alexander Skeltved . . . . . . . . . . . . . . . 20
An illustration of the leader tip with the streamer zone. In the streamer
zone electrons of keV energies can accelerate to MeV energies [Mallios
et al., 2013]. Image credit: Alexander Skeltved . . . . . . . . . . . . . 21
Simulation of the feedback process in an electric field of 750 MV/m
over 150 m. Top panel: t < 0.5 µ s, middle panel: t < 2 µ s, lower
panel: t < 10 µ s. Black is electrons (1 per 1000 are drawn) and blue is
positrons. Figure adapted from Dwyer [2007]. . . . . . . . . . . . . . . 23
Attenuation cross sections for high energy photons in air. At low energies the photoelectric absorption is dominating, at high energies the
pair production is dominating and at intermediate energies the attenuation is dominated by the Compton scattering. . . . . . . . . . . . . . . 26
An illustration of the bremsstrahlung process. An electron with momentum p1 is decelerated in the Coulomb field of a nucleus and exit
the field with momentum p2 . The nucleus receives the momentum q in
the process and the energy lost by the electron is emitted as a photon
with energy and direction k. . . . . . . . . . . . . . . . . . . . . . . . 27
The position of The Reuven Ramaty High Energy Solar Spectroscopic
Imager (RHESSI) nadir at the time of TGFs. The gray areas are the
areas within 370 km from the coast. It can be seen that most TGFs
occur over land or coastal areas. The figure is adapted from Splitt et al.
[2010]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The location of the Fermi nadir and the probable source lightning show
that most TGFs are originating from coastal regions even if the satellite
is inland or above the ocean. The circles marks the location of the
source lightning and the start of the line marks the Fermi nadir. The
blue circles are TGFs found from the continuous data collection and
the red circles are triggered TGFs. The figure is adapted from Briggs
et al. [2013]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The distance between the RHESSI nadir at the time of TGFs and the geolocated lightning from The World Wide Lightning Location Network
(WWLLN) for the years 2002-2011. As can be seen the source density
is largest close to the satellite nadir. This is as expected as farther distances and more atmosphere between the location of TGF production
and the satellite makes more TGFs fall below the detectability threshold of the instrument. . . . . . . . . . . . . . . . . . . . . . . . . . .
The diurnal distribution of TGFs from the first RHESSI catalog and
the lightning density from LIS/OTD. The boxes indicate the lightning
density, the black is oceanic TGFs, the dark gray is inland TGFs and
the light gray is the combined land and coastal TGFs. It is clear that at
least the land and coastal TGFs follow the same diurnal distribution as
lightning. The figure is adapted from Splitt et al. [2010]. . . . . . . .
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viii
LIST OF FIGURES
5.5
This map is showing how the TGF/lightning ratio, based on RHESSI
TGFs, is changing geographically relative to the median ratio. 0 is
median ratio, blue is a lower than median TGF/lightning ratio, red is a
higher than median ratio. It can be seen that the ratio is significantly
higher in America and Asia than in Africa. The full description of the
figure can be found in Nisi et al. [2014](Paper 3 of this thesis) . . . .
5.6 Latitudinal difference in tropopause pressure for TGFs occurring in
June-July-August and in December-January-February. The lower pressure in DJF is due to a stronger Dobson-Brewer circulation in these
months. Figure is from Nisi et al. [2014]. . . . . . . . . . . . . . . .
5.7 Fluence distribution of the first (red) and second (black) RHESSI catalog TGFs. As the new catalog expands the distribution to lower fluences, it is clear that we might just see the tip of the iceberg and are
limited by the detection threshold of the instrument. Figure is adapted
from Gjesteland et al. [2012]. . . . . . . . . . . . . . . . . . . . . . .
5.8 The measured fluence distribution go the second RHESSI catalog
(gray) and the dead-time corrected fluence distribution (black). If the
power law shown in the figure is expanded to lower fluxes it is clear
that a larger number of events would be expected from the soft (gray)
distribution than the hard (black) distribution. Figure is from Østgaard
et al. [2012](Paper 1 of this thesis). . . . . . . . . . . . . . . . . . . .
5.9 The photon altitude distribution for a TGF for an initial production altitude of 12 km. The electric field is stretching over an atmospheric depth
of 87 g/cm2 which corresponds to around 9.7-12 km at this altitudes.
The figure is adapted from Smith et al. [2011a] . . . . . . . . . . . .
5.10 Modeling results of how the angle of observation and the half angle of
the emission cone affects the fluence observed at a satellite. a) shows
an illustration of the setup, α is the observation angle and θ is the
half angle of the emission cone. b) shows the number as a function
of the observational angle. The source altitude is put at 15 km. The
solid curve is showing how the number change if only considering the
reduction in fluence with distance. The dashed-dotted curve is for 60
degrees emission angle, the dashed curve for 40 degrees emission half
angle and the dotted curve for 20 degrees emission half angle. It is clear
that the number of photons drop significantly (but not to 0) outside the
emission cone. All the photons outside the cone is either produced by
annihilated positrons or they are Compton scattered away from their
initial direction. The figure is adapted from Gjesteland et al. [2011] .
5.11 The fluence distribution of a selection of the second RHESSI catalog
TGFs (red) and the fluence distribution of the same selection when corrected for maximum production altitude and distance from the satellite.
This shows that the correction change the distribution to a softer distribution, and that it is important to project the fluence back to the source.
The figure is adapted from Nisi et al. [2014]. . . . . . . . . . . . . . .
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List of papers
1. Østgaard, N., Gjesteland, T., Hansen, R. S., Collier, A. B., and Carlson, B., The
true fluence distribution of terrestrial gamma flashes at satellite altitude, Journal
of Geophysical Research, 117(A03327), doi:10.1029/2011JA017365, 2012
2. Hansen, R. S., Østgaard, N., Gjesteland, T., and Carlson, B., How simulated
fluence of photons from terrestrial gamma ray flashes at aircraft and balloon
altitudes depends on initial parameters, Journal of Geophysical Research 118,
doi:10.1002/jgra.50143, 2013
3. Nisi, R. S., Østgaard, N., Gjesteland, T., and Collier, A., An altitude and distance
correction to the initial fluence distribution of TGFs, Journal of Geophysical Research, 2014
x
List of papers
Acknowledgements
I would like to thank. . .
xii
Acknowledgements
Chapter 1
Introduction
In 1991, NASA launched the Compton Gamma Ray Observatory (CGRO) satellite.
On board was the Burst and Transient Source Experiment (BATSE), whos goal was to
measure cosmic gamma ray bursts. In 1994 Fishman et al. [1994] reported on another
phenomenon observed by the instrument. Short bursts of gamma rays with duartions
much shorther than the cosmic gamma rays were seen to originate from the Earth. The
phenomenon was named Terrestrial Gamma Ray flashes (TGFs).
This was the start of the TGF research and 20 years on, the TGFs are still not fully
understood. We know that the source of the TGFs are somewhere inside thunderstorms
and that they result from a large number of high energy electrons that produce high
energy photons through bremsstrahlung. However, we do not know exactly where in
the thunderstorm; at what altitude are TGFs produced, and is the production occuring
inside or outside of the actual lightning? We do not know how many electrons are
actually needed for the production of the TGFs. Furthermore, we do not know the full
acceleration process of the electrons.
In my work with this PhD, I have mainly worked with establishing the source properties. If we can constrain these further, we will be able to answer more of the questions
concerning the production process. One major question is the fluence distribution of
the TGFs. Variations in the clouds and in lightning can be expected to create variations
in the fluence of TGFs. In paper 1 of this thesis, we investigated how this fluence distribution lookes at satellite altitude. Later, in Paper 3, we adressed how the fluence would
change if propagated back to the source. As we do not know the actual source location and altitude of the TGF, this was only possible to do approximately, but the result
clearly shows that the fluence change signinficantly when propagated to the source. In
Paper 2, we adressed the possibility of doing measurements that would make us able
to get more knowlege of the TGF initial properties. We show that measurements made
at aircraft and balloon altitudes are heavily affected by the initial source properties, but
that care have to be taken to be able to separate the effects of one property change to
another. A parallell study that is not yet published is a modelling of the bremsstrahlung
process at TGF energies. The bremsstrahlung models that excist are all based on an
assumption that we do not know the effect of for TGFs. I want to show how big the
error is in order to improve the models and be able to say more about the high energy
electrons that creates the TGFs.
In this dissertation, I will first present the observations we have of TGFs and connected lightning. Subsequently, I present the two main production theories for TGFs
2
Introduction
and explain how they are different. I then present the modelling efforts that I have been
involved in before looking closely at the initial source properties of TGFs. I explain
what we know and do not know and how new knowledge of the initial source properties will help us solve several of the issues connected to the TGF production. Lastly are
my papers and a summary of each of them.
Chapter 2
Observations
So far, TGFs have mainly been measured by space borne instruments. However, observations have also been made by airborne detectors and more space and airborne
instruments are in the planning. The main problem with the data already available, is
that almost all the instruments are designed to detect gamma rays from the universe or
the sun. These gamma rays have much longer time scales and different energies than
TGFs. Very early, a connection between TGFs and lightning was established, which
made reliable lightning detection essential. The main measurements and observational
methods for TGFs, together with the main instrumentation for lightning detection are
presented first in this chapter. In the last section x-rays from lightning and laboratory
sparks are discussed.
2.1 Satellite observations of TGFs
2.1.1 The Burst and Transient Source Experiment
The Burst and Transient Source Experiment (BATSE) on board the The Compton
Gamma-Ray Observatory (CGRO) was the first instrument to detect TGFs [Fishman
et al., 1994]. The instrument was designed to study cosmic Gamma-Ray Burst (GRB)
and consisted of 8 Sodium Iodide (NaI) detectors of 2000 cm2 each, one on each corner of the satellite. Having the detectors positioned this way allowed for determining
the direction of the incoming gamma rays, which is how some gamma rays were found
to originate from the Earth. BATSE was sensitive to photon energies between 20 keV
and 2 MeV and stored the photons in 4 energy channels (20-50keV, 50-100keV,100300keV and >300keV) [Fishman et al., 1994; Grefenstette et al., 2008]. In the 9 years
of the satellites lifetime, it detected 78 TGFs, with each TGF consisting of around 100
photons [Nemiroff et al., 1997]. The large number of photons in each TGF enabled
spectral analysis of individual TGFs, which was used to constrain some of the initial
conditions of TGFs [Østgaard et al., 2008]. This is described further in Chapter 5. The
trigger algorithm had a minimum trigger window of 64 ms, which is much longer than
the TGF duration. This means that the instrument only got a significant signal over the
background counts for the longest and strongest TGFs [Dwyer et al., 2012a]. As early
as in the first paper by Fishman et al. [1994], the connection between TGFs and thunderstorms was established, as TGFs was only detected when the satellite was passing
over an area with thunderstorms.
4
Observations
Grefenstette et al. [2008] showed that BATSE was heavily affected by dead time.
Dead time is the time after a photon hit that the instrument is dead to new photons
due to the processing of the first photon. If the time between individual photons are
larger than the dead time, the instrument will be able to detect all photons, but if the
next photon hit the detector within the dead time, the photon will not be registrerd.
In Figure 2.1 the two main types of dead time is illustrated. The top panel shows the
time of the incoming photons as red lines. The second panel shows the response of an
unparalyzable detector. The black boxes illustrate the dead time, while the red lines
are the registrerd photons. In a unparalyzable detector, a photon hitting within the dead
time is not counted, but also not affecting the ongoing dead time. The lower panel
illustrates a paralyzable detector. A photon that hit the detector within the dead time
of this detector will start a new dead time. This may lead to a situation where no new
photons can be detected before the time between photons are reduced to a time longer
than the dead time.
Incomming photons
Time
Nonparalyzable
Dead
Live
Time
Paralyzable
Dead
Live
Time
Figure 2.1: An illustration of the two main detector responses to photons hitting the detector
when the detector is dead. The top panel shows the time of the incoming photons, the middle
panel shows the response of a nonparalyzable detector, and the lower panel shows the response
of a paralyzable detector. The red lines mark the photons that are registrered by the detector.
The paralyzable detector start a new dead time for photons hitting the detector within the
deadtime of a previous photon. This can make the detector dead for long periods of time if
new photons are arriving too short after one another.
In a nonparalyzable detector, the total dead time is proportional to the measured
counts (m), and the number of measured counts is related to the actual counts (n) as
n
follows: m = 1+n
τ , where τ is the dead time [Knoll, 2000, Chap. 4.7]. For a paralyzable
detector, the number of measured counts are proportional to the number of true counts
and are found to be: m = n × exp(−nτ ) [Knoll, 2000, Chap. 4.7]. An example of
measured vs actual counts in a paralyzable and a nonparalyzable detector is shown in
Figure 2.2. The figure also shows how, for the paralyzable detector, one measured
number of photons can be produced by two different numbers of true photons.
BATSE is a paralyzable detector, with high energy photons creating longer dead
times than low energy photons [Grefenstette et al., 2008]. Grefenstette et al. [2008]
investigated the preflight data of BATSE and found that the dead time can be expressed
k
as: τ = α ln( k0p ), where α =0.75 µ s is the signal decay time, k p is the energy of the
incoming photon and k0 =5.5 keV is the reset level of the detector. This equation shows
5
Id
ea
l
2.1 Satellite observations of TGFs
Nonparalyzable
Paralyzable
n1
n2
Figure 2.2: An illustration of the number of measured counts vs true counts in a paralyzable
and a nonparalyzable detector. The ideal detector would measure the true number of photons,
but the actual detectors measure less than the actual number when the number of photons are
more than a few tens in this example. Note that for the paralyzable detector, the measured
number of photons can relate to two different numbers of true photons.
that a TGF with a hard spectrum (many high energy photons) will be most affected by
the instrument dead time.
2.1.2 The Reuven Ramaty High Energy Solar Spectroscopic Imager
The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite was
launched in 2002 to investigate solar flares, and is still operating. The satellite was
launched into a low Earth orbit at around 500 km altitude and with an inclination of
38 degrees. This means that the satellite cover most of the tropics and subtropics, excluding most of South America where the back ground radiation is very high due to
the South Atlantic Anomaly. The effective area of RHESSI to photons above ∼100
keV was initially ∼200-300 cm2 , but the sensitivity was significantly reduced after radiation damage to the instrument in 2005/2006 [Grefenstette et al., 2009]. Even the
original sensitivity is significantly smaller than BATSE, and RHESSI measures typically less than 30 photons per event [Gjesteland et al., 2012]. RHESSI is sensitive to
photons with energies from 30 keV to 20 MeV and transmits the data of all individual
photons to ground [Smith, 2002]. Because of the transmission of all photon data, there
exists two catalogs of RHESSI TGFs from ground search using two different search algorithms. The first was made by Grefenstette et al. [2009] and consists of about 900
TGFs between 2002 and 2011, the second catalog by Gjesteland et al. [2012] use a
reduced significance level for a signal to be considered a TGF and consists of ∼2500
6
Observations
TGFs from the same period. This means that Gjesteland et al. [2012] get more of the
weak TGFs, but at the expense of a higher probability for counting statistical fluctuations as TGFs. The limit that Gjesteland et al. [2012] use is a probability of 10−11 that
the signal is a statistical fluctuation and not a TGF. With 1011 search bins per year, this
gives one expected false TGF per year. The RHESSI satellite also suffers from dead
time. RHESSI is a semi paralyzable detector that is paralyzable if the photons are less
than 0.84 µ s apart, and nonparalyzable for photons arriving more than 5.6 µ s and less
than 9.6 µ s apart [Grefenstette et al., 2009]. This means that the satellite is paralyzable, but only for fluxes not known to excist in TGFs. Since the RHESSI detectors has a
much smaller area than BATSE, RHESSI are rarely paralyzed even if the dead time for
paralyzation of RHESSI is longer than for BATSE. Østgaard et al. [2012] did a Monte
Carlo simulation of the RHESSI dead time for a TGF detected by RHESSI on May 2.
2005, and found that for up to 15 counts, RHESSI are mostly able to count all photons,
while for higher count rates some photons were not registrerd. Figure 2.3 shows the results of the MC modeling by Østgaard et al. [2012], the duration of the TGF was 361
µ s and it consisted of 30 photons. The gray areas are error bars, found by repeating the
same simulation 100 times. For this TGF with 30 measured photons, the true number
was probably between 35 and 45 photons hitting the detector. Østgaard et al. [2012] is
Paper 1 of this thesis.
Figure 2.3: The dead time of RHESSI as found from Monte Carlo simulations of a TGF
detected on May 2. 2005. The duration of the TGF was 362 µ s and the TGF consisted of 30
measured photons. The gray error bars are calculated from repeating the simulation 100 times.
The figure shows that the RHESSI instrumentation is mostly able to detect all photons up to
around 15 photons per TGF. For higher fluxes of photons RHESSI will be affected by the dead
time, and not all photons detected. For this TGF with 30 measured photons, the true number
was probably between 35 and 45 photons. This figure is adapted from Østgaard et al. [2012]
(Paper 1 of this thesis).
2.2 Airborne and ground observations of TGFs
7
2.1.3 Astrorivelatore Gamma a Immagini Leggero
The Astrorivelatore Gamma a Immagini Leggero (AGILE) is an Italian mission designed to measure gamma rays from the universe. The satellite was launched into a
low-Earth orbit with an inclination of only 2.5 degrees, which means that it has a very
good cover of the equatorial region. The Mini-Calorimeter (MCAL) measure photons
from 350 keV to 100 MeV and have a effective area of around 500 cm2 [Marisaldi et al.,
2010a]. This area is aboth 2 times as large as RHESSI, but significantly smaller than
BATSE. Between March 2009 and July 2012, AGILE detected 308 TGFs with photon
energies up to 30 MeV, each TGF consisting of a few tens of photons [Marisaldi et al.,
2014]. It has also been reported signals with individual photon energies up to 100 MeV,
but it is unclear if this is from TGFs [Tavani et al., 2011].
2.1.4 Fermi Gamma-ray Space Telescope
The Fermi Gamma-ray Space Telescope (Fermi) is a NASA satellite launched in 2008.
The main instrument for detecting TGFs is The Gamma-ray Burst Monitor (GBM).
This instrument consists of 2 Bismuth Germanate (BGO) detectors of 200 cm2 each
and 12 NaI detectors of about 100 cm2 each and can detect photons between 8 keV and
40 MeV [Meegan et al., 2009]. The TGFs consists of ∼50 or more photons, making
spectral analysis of single TGFs possible [Briggs et al., 2013]. During the first years
of data collection, Fermi was triggered by a significant increase in the NaI detectors
only [Briggs et al., 2010], but later the BGO was also included in the trigger algorithm
[Fishman et al., 2011]. This significantly increased the number of TGFs detected as the
NaI detectors only measure photons up to a few hundreds of keV and the background
is significantly higher for the NaI detectors than for the BGO detectors [Briggs et al.,
2013; Fishman et al., 2011]. The Fermi use a trigger window of 16 ms. This is significantly less than BATSE (64 ms), but still 20-100 times larger than the duration of
typical TGFs [Briggs et al., 2013]. In 2010 Fermi started downloading continuous data
for times and locations known to have a high number of TGFs. Between July 2010 and
August 2011, 1036.7 hours of data was transmitted to ground. From a ground search
of the data, 423 TGFs were detected [Briggs et al., 2013]. The large number of TGFs
with high count rates makes this the most extensive set of TGF measurements so far.
2.2 Airborne and ground observations of TGFs
2.2.1 Airborne Detector for Energetic Lightning Emissions
The Airborne Detector for Energetic Lightning Emissions (ADELE) is the only instrument that has detected TGFs from low altitudes. The instrument was mounted on The
Gulfstream V jet (GV) operated by The National Center for Atmospheric Research
(NCAR). And it was flown for about 37 hours at around 14 km altitude above thunderstorms in Florida and Montana in August-September 2009. During these flights it
detected one TGF, and passed closer than 10 km from 1213 individual lightning flashes
[Smith et al., 2011a,b]. The significance of these results are discussed in connection to
the number of TGFs in section 5.2.
8
Observations
2.2.2 Detection from ground
Due to the density of the atmosphere at low altitudes, gamma rays can only travel for
very short distances before being attenuated by the air. This means that detectors have
to be positioned close to the lightning to detect TGFs on ground. Dwyer [2004] and
Dwyer et al. [2012b] report on one TGF each, that is observed from ground. In Dwyer
[2004], the source lightning was a rocket triggered lightning. The TGF lasted for about
300 µ s and consisted of 227 photons with individual energies of up to 11 MeV. The
gamma rays were observed during the initial stage of the triggered lightning, about 40
ms into the triggering. The timing of the gamma rays made Dwyer [2004] conclude
that the gamma rays originated from the inside of the cloud at an altitude of a few km.
The TGF recorded by Dwyer et al. [2012b] was from a natural lightning. The TGF
consisted of 19 gamma photons, the most energetic photon had an energy of at least
20 MeV. The TGF lasted only 52.7 µ s and occurred during the return stroke of the
lightning. The energy spectrum and duration of these two TGFs is what distinguish
them from x-rays commonly observed from lightning.
2.2.3 Radio waves from TGFs
As the TGFs are produced by a large amount of high energy electrons, these will create
a current that emits a electromagnetic pulse. Connaughton et al. [2013] estimated the
radiated effect from TGFs and found that especially short TGFs would radiate enough
energy to be measured by Very Low Frequency (VLF) receivers. For longer events,
they argued that the combined radiated effect from TGFs and lightning might make
the probability for observing TGF-producing lightning greater that non-TGF-producing
lightning. About the same time as this was published, Østgaard et al. [2013] investigated a RHESSI TGF above Lake Maracaibo and found that the detected VLF signal
could probably be related to the TGF electrons. This analysis was made possible by
the fact that the TGF producing lightning was detected by an optical signal in addition to VLF. In the next section we will see that also lightning detection is made by
radio waves and one have to be extra carful when assigning observed radiowaves to the
lightning as it may be produced by the TGF itself.
2.2.4 Observability of TGFs by aircraft and balloon
Hansen et al. [2013] (Paper 2 of this thesis) investigated the observability of the TGFs
by balloons and aircrafts. The photons from TGFs were modeled by using the Monte
Carlo model of photon transport that will be described in section 4.1. The expected
measurements from a balloon or aircraft was then estimated by placing a detector area
at balloon (35 km) and aircraft (14-20 km) altitudes and at different horizontal distances
from the source. At all altitudes, the expected observation was very sensitive to the
horizontal distance from the source, the initial altitude and the initial number of source
photons. For low observational altitudes, the expected fluence was also very sensitive
to the distribution in initial altitude and direction of the initial photons. This result
might be useful in the planning of new missions as well as in the analysis of the future
observations.
2.3 Observations of lightning
9
2.3 Observations of lightning
Lightning creates a large current that emits a powerful electromagnetic pulse that can
be used to measure lightning. From ground, this is widely used. From space, large
areas can be observed by one single satellite, this is utilized to look for the optical
signals from lightning. All the different observational methods have limitations, but
can complement each other.
2.3.1 Low Frequencies
Electromagnetic waves in the Very Low Frequency (VLF) and Extreme Low Frequency
(ELF) range is the ones mainly used for lightning detection. This is because these waves
can travel for long distances in the atmosphere with little or no absorption due to the
wave guide created between the conducting Earth and the conducting ionosphere. Even
at long distances from the lightning, VLF and ELF receivers can detect the electromagnetic wave with little or no distortion. As long as more than three receivers detect the
same lightning, the location of the lightning can be determined through triangulation.
The World Wide Lightning Location Network (WWLLN) is a global network, covering most of the geographic areas with large numbers of lightning. WWLLN had
an overall global efficiency of around 2 % in 2007, increasing to about 6 % in 2009,
but with large local variation [Abarca et al., 2010]. The detection efficiency is about
two times higher for lightning to the ground than for lightning occurring inside the
clouds and the efficiency is much higher for large current discharges than for low current discharges [Abarca et al., 2010; Collier et al., 2011; Connaughton et al., 2010].
Other networks include The National Lightning Detection Network (NLDN) and The
Atmospheric Weather Electromagnetic System for Observation, Modeling, and Education (AWESOME) and a detector at Duke University [Cohen et al., 2010a,b; Cummer,
2005; Cummer et al., 2011; Kulak et al., 2012]. Due to the low frequency and long distances, the low frequency networks are not able to determine the altitude of the lightning discharge or the polarity of the lightning. This is possible with higher frequency
networks.
2.3.2 High Frequency and Very High Frequency
High Frequency (HF) and Very High Frequency (VHF) waves from lightning can only
travel short distances in the atmosphere before they are attenuated, but they are less
distorted when detected by the receiver. This enables a fairly accurate estimation of
the position, current direction, current magnitude and current moment of the lightning.
The Los Alamos Spheric Array (LASA) and The Lightning Mapping Array (LMA)
have been extensively used for TGF research [Lu et al., 2010; Shao et al., 2010; Stanley
et al., 2006]. As the receiver has to be close to the actual lightning, only a very small
part of the total amount of lightning is detected by HF-receivers.
2.3.3 Satellite measurements
The Lightning Imaging Sensor (LIS) on board The Tropical Rainfall Measuring Mission (TRMM) and The Optical Transient Detector (OTD), which preceded LIS, are
10
Observations
optical satellite-carried lightning detectors. Within their field of view these instruments
have very good detection efficiency. LIS and OTD can give time, position, duration
and approximate intensity of the lightning, but can not say anything about the current
direction or magnitude due to the large distance from the lightning [Boccippio et al.,
2000; Christian, 2003].
2.4 X-rays from lightning and laboratory sparks
2.4.1 X-rays from lightning
Dwyer et al. [2003] were the first to reliably confirm x-rays from lightning. Before this,
for instance Moore et al. [2001] had also measured x-rays coincident with lightnings,
but they were not able to fully confirm the lightning as the source of the x-rays. Figure
2.4 shows the x-rays from a lightning reported by Dwyer et al. [2004]. The time 0, is
the time of the start of the optical return stroke. The red diamonds are the recorded
data, the black line is the detector response. This shows several bursts of x-rays with
energies of more than 100 keV, lasting on the order of 1 µ s. The last few pulses before
the return stroke saturated the detector, probably because the source of these bursts
were closer to the detector [Dwyer et al., 2004].
Figure 2.4: X-rays from a triggered lightning reported by Dwyer et al. [2004]. The red diamonds are the recorded data, the black curve is the detector response. This shows several
µ s-duration bursts of energetic radiation just before the lightning return stroke (t=0).
Since this discovery, this type of x-rays have been shown to be connected to the
stepping process during the initial part of the lightning. It has also been seen to be
colocated with the streamer tip ?his will be further discussed when looking at the lightning process in section 3.2.2.
2.4.2 X-rays from laboratory sparks
In 2005, Dwyer et al. [2005] discovered that also large laboratory sparks produce short
x-ray bursts. They had a 1.5 MV Marx circuit and produced discharges between 1.5
and 2 m long in air at 1 atmosphere pressure. All of the 14 discharges they investigated
produced x-rays with energies between 30 and 150 keV. Dwyer et al. [2008] used the
same experimental setup and investigated more than 200 sparks. They measured x-rays
2.4 X-rays from lightning and laboratory sparks
11
with individual photon energies of up to 300 keV, in around 70 % of the sparks of
negative polarity and in around 10 % of the sparks of positive polarity. Using spherical
electrodes with diameters of 12 cm they also excluded the possibility of the electric
fields of the electrodes influencing the x-ray production.
Later, Kochkin et al. [2012] used a camera with very high shutter speeds to investigate how the spark looked when x-rays were emitted. Figure 2.5 shows photos of a
positive polarity spark at different times, together with the x-ray signal from a LaBr detector. The figure shows how the x-rays are created just before the streamers from the
two electrodes connect. This is probably because this is the location and time when the
electric field is largest. The theory behind the acceleration process will be discussed in
section 3.2.2 and 3.3.
In these experiments Kochkin et al. [2012] used a Marx generator that could produce
up to 1 MeV potential across a gap of approximately 1 m. They measured x-rays with
single photon energies of about 200 keV. In a total of almost 1000 sparks they also
showed a significant dependence on location of the LaBr detector. In one position they
measured x-rays in all the sparks, while in another position the detection rate was down
to about 25 %.
This experimental setup at Eindhoven University of Technology has also been use
to investigate if all sparks create x-rays. This might be important in order to establish
the total number of TGFs and will be further discussed in section 5.2.
12
Observations
Figure 2.5: Photos of a positive polarity spark using a camera with very high shutter speed at
different points during a spark development. The panel at the bottom show the times of the
photos, the voltage across the gap (U), the current on the high voltage electrode (IHV ), the current of the ground electrode (IGND ) and the signal from x-rays as detected by a LaBr-detector.
The two arrows in the first photo mark the electrode tip (lower arrow) and the streamers created on the top of the electrode disk. The photos show that the x-rays are created just before
the streamers from the two electrodes connect.
Chapter 3
Theories of production
TGFs are recognized as being bremsstrahlung photons produced by relativistic electrons. And it is widely accepted that the electrons are accelerated in an electric field
related to thunderclouds. For an electron to create a photon of tens of MeV energy the
electron have to be accelerated in an electric field with a potential of at least several tens
of MV. In this chapter, a description of the acceleration process will be given, before an
overview of thunderstorms and lightning will be presented. Next, the two leading theories of TGF production is introduced. The main differences between the two theories
are the location of the accelerating electric field and the origin of the initial electrons.
Finally, a discussion of the bremsstrahlung process will be presented. Bremsstrahlung
is the process in which the electron decelerate and emits a photon.
3.1 Relativistic Runaway Electron Avalanche
The Relativistic Runaway Electron Avalanche (RREA) process is a result of the the
friction force in the air changing with energy in combination with electron-electron
(Møller) scattering. Figure 3.1 shows the friction force for electrons in air at standard
atmospheric pressure. The friction force is increasing with energy up to about 100 eV,
before decreasing with energy. This means that if an electron with initial energy εth
that is higher than around 100 eV, which is the energy corresponding to the maximum
friction force, experience an electric field higher than the corresponding field E, the
electron can accelerate to relativistic energies. The initial high energy electron is usually referred to as a seed electron. This process was first described by Wilson [1924]
and are known as the Wilson runaway.
If a runaway electron collides with another electron, the second electron can receive
enough energy to also be in the runaway energy range (ε >εth ) and accelerate to high
energies. If this is allowed to continue it will result in an avalanche of relativistic
electrons with the number growing exponentially with time. This has been named
Relativistic Runaway Electron Avalanche (RREA) and has been extensively discussed
by Babich et al. [2007], Dwyer and Smith [2005], Roussel-Dupré et al. [1994] and
Roussel-Dupré and Gurevich [1996] among others.
The number of electrons accelerated in a uniform field can be expressed as:
FRREA = F0 exp(z/λ )
(3.1)
14
Theories of production
eEc
eE
eEk
eEst-
eEst+
eEth
eEb
εth
Figure 3.1: Friction force for electrons in air at standard surface pressure. If an electron
with energy of εth experience an electric field greater than or equal to E it will accelerate to
relativistic energy. Eb and a seed electron of ε ≈ 1 MeV is the weakest electric field that can
give a runaway electron. The other electric fields in the figure is explained in the text. Figure
adapted from Dwyer et al. [2012a]
where F0 is the initial number of seed electrons, z is the distance from the start of the
avalanche and λ is the avalanche length. Over the entire avalanche region, the number
of electrons will become:
FRREA = F0 exp(L/λ )
(3.2)
where L is the total size of the avalanche region.
λ is defined as where the number of initial photons have increased by a factor e
[Dwyer et al., 2012a]. Empirically from models, we have λ = 7.3MeV
eE−Fd , where Fd is
the average energy loss rate for the electrons in the direction of the avalanche [Dwyer,
2003].
The electric field Eb ≈ 2 × 105 V/m in Figure 3.1 is the weakest electric field that
can give a runaway electron. To get a RREA the electric field has to be at least Et h=
2.8 × 105 V/m. This is due to the electrons giving off energy to the secondary electrons
in the Møller scattering process.
When the avalanche has been allowed to work for several avalanche lengths, the
energy spectrum of the electrons (runaway electrons per unit energy) in a RREA is
given as
dF
FRREA
−ε
fre =
=
exp
(3.3)
dε
7.3MeV
7.3MeV
where ε is the energy of the electron [Dwyer et al., 2012a]. Note that this means that
the average energy of the electrons will be 7.3 MeV.
3.2 Thunderstorms and lightning
15
If the electric field is higher than the critical electric field Ec on Figure 3.1, all
electrons independent on initial energy can be accelerated to relativistic energies by the
electric field. Ec has a sea equivalent value of about 26 MV/m [Moss et al., 2006]. This
electric field is much larger than the electric field required to create a breakdown and
can thus only exist in a small localized region.
3.2 Thunderstorms and lightning
Already in the first report on TGFs by Fishman et al. [1994], the connection to thunderstorms was established . Thunderstorm electrification is a result of strong convection of
warm air causing ice crystals present in the cloud to collide with groupels [Saunders,
2008]. In this collision process, water present on the surface of the grouple freeze onto
the ice crystal. Due to different growth rate of the particles one of the particles will
carry more negative surface charge than the other. In the collision the charge present
in the point of contact will distribute equally between the two particles, resulting in the
two types of particles carrying a net charge. Which particle that grows fastest and that
has the most negative surface charges is depending on the temperature and water content of the air. The transition between the two is about ??. Due to the need for warm
and moist air, most lightning occur over land, over regions where there is no desert and
in the afternoon local solar time.
The main charge configuration in a thundercloud is often described as a tripole with
a main positive charged region on top, a main negative charged region below and a
small positive region at the bottom. Due to the charge transfer between ice and groupels
changing with temperature, the main negative region is usually where the temperature
is between -5 °C and -25 °C [Saunders, 2008]. The exact location is determined by the
liquid water content of the air. The main positive and main negative charge regions are
a direct result of the collisions between the ice and groupels, while the lower positive
charge region is a screening layer that develops between the main negative charged
region and the neutral atmosphere. An illustration from Stolzenburg et al. [1998] is
presented in Figure 3.2, showing that the commonly measured charge structure is much
more complex than the simple tripole. Generally, the updraft region has a quadrapole
structure with an extra negative screening layer on top in addition to the basic tripole
structure, and the downpour region have more layers [Stolzenburg and Marshall, 2008;
Stolzenburg et al., 1998].
The measurements of electric fields in thunderstorm are mainly obtained by balloons or aircrafts flying through a thunderstorm. A typical balloon sounding of the
electric field and voltage is shown in Figure 3.3. This sounding was reported by Marshall and Stolzenburg [2001]. Using a one-dimensional approximation to Gauss law
they also estimated the altitude and polarity of the charge regions, shown on the right
side of the figure. The strongest electric fields in a thundercloud is usually around 15×105 V/m and commonly stretches over a couple of km vertically [Stolzenburg and
Marshall, 2008; Williams, 2006]. The typical measured potential between the main
positive and the main negative region is around 60-80 MV, and a maximum measured
potential around 100 MV [Marshall and Stolzenburg, 2001]. The estimated maximum
potential available for intra cloud lightning is shown to be slightly higher, at around
130 MV [Marshall and Stolzenburg, 2001]. The maximum available potential for intra-
16
Theories of production
Figure 3.2: Illustration of the charge structure of thunderstorms adapted from Stolzenburg et al.
[1998]. The cloud has a main negative at around -25 °C and a main positive above that. In
addition the screening charges create a basic quadrapole charge structure in the updraft region.
In the downpour region more layers are present.
cloud lightning is considered to be the potential difference between the nearest relative
maxima and minima voltage within the cloud.
There are two main types of lightning. The Intra Cloud (IC) lightning is a discharge between charged regions in the cloud or between one cloud and another. The
Cloud to Ground (CG) lightning is transferring charge between the thundercloud and
the ground. A negative lightning is defined as a breakdown process bringing negative
charge downward, positive lightning will bring negative charge upwards.
3.2.1 Initiation of lightning
Very little is known about the actual initiation of lightning. The requirement is a region
where the electric field is strong enough to ionize the air at a higher rate than the attachment processes for the electrons. This required field is known as the conventional
breakdown electric field Ek and has a value of ≈3 MV/m at 1 atmosphere pressure, see
Figure 3.1. However, the maximum electric field in a thunderstorm is usually an order
of magnitude lower than this, suggesting that other processes are involved as well.
The first element of a lightning is the streamer, which is a filamentary discharge
propagating as an ionizing wave that represent a common electrical breakdown process
at ground level atmospheric pressure [Celestin and Pasko, 2011]. A streamer need an
electric field of Ek to be initiated, but the field can be very small in size. All the main
lightning initiation theories include the role of the hydrometeors (water droplets and ice
crystals). Hydrometeors have a large dielectric constant making them act as conductors
in the electric field of a thundercloud, and the hydrometeors will become polarized.
The role of water droplets was investigated by Griffiths and Latham [1972], who found
that an ambient electric field of about Ek /3 was needed in order to initiate a streamer.
3.2 Thunderstorms and lightning
17
Figure 3.3: Measured electric field (solid curve) and integrated voltage (dashed) for a balloon
sounding on August 1. 1984. Approximate altitude and polarity of the charge regions of the
cloud are shown at the right. This was inferred using a one-dimensional approximation to
Gauss law. The figure is adapted from Marshall and Stolzenburg [2001].
Later, Petersen et al. [2006] showed that ice crystals seems to be more important than
the water droplets. Ice crystals can grow much longer than water droplets without
breaking up and Foster and Hallett [2002] showed that the ice crystals align with the
electric field of the clouds. In this way, the ambient electric field can be much weaker
and still initiate streamers. The altitude of lightning initiation also match well with the
area with large ice growth, further supporting this theory [Petersen et al., 2006].
After RREA was established, Gurevich et al. [1992] suggested that the secondary
ionization of cosmic-ray air showers accelerated through the RREA process could create a small electric field with field strengths above Ek and initiate a streamer. This
theory was further developed and discussed by Gurevich et al. [1997] and Gurevich
et al. [1999]. The two main problems with this theory is the relative rarity of powerful enough cosmic-ray air showers and the required size of the avalanche to initiate a
streamer.
Dwyer [2005] proposed yet another theory for the initiation of the streamer. As
soon as the electric field in the thundercloud exceeds Eb , some electrons will start to
accelerate and create secondary electrons locally. This might then further increase the
electric field and hence the acceleration of new electrons. This process was named
the runaway breakdown as the process is seen from models to be able to discharge the
electric field without optical lightning. Figure 3.4 is adapted from Dwyer [2005] and
shows how the process is developing in models. A negative charge region is placed at
18
Theories of production
the bottom of the figure, a positive on the top. The black arrows shows the trajectories
of runaway electrons. After a period on the order of seconds from the start of the
process, the electric field on can reach a field strength of Ek /3. On Figure 3.4 the field
on the tip has reached a value of 450 kv/m which corresponds to Ek /3 or 1000 kv/m
at 1 atmosphere pressure. This means that in a presence of a hydrometeor, this could
initiate a streamer. This was further investigated by Dwyer [2012] and Liu and Dwyer
[2013].
Figure 3.4: A simulation of the runaway breakdown process from Dwyer [2005]. A positive
region is placed on top of the figure, and a negative on the bottom. If this ambient field is larger
than Eb that is the limit for runaway breakdown, some electrons will start accelerating towards
the positive region. These accelerating charges will create ionization and hence increase the
field in a small region. The field will lead to more acceleration and more ionization and hence
the process will escalate. In this figure the black arrows depicts the trajectories of the runaway
electrons and the electric field strengths at the 1 atmosphere equivalent are shown in colors.
In the white region where the electric field is around 1 MV/m a streamer might form if a
hydrometeor is present.
3.2.2 Streamer and leader process
After the first initiation of a streamer, the ionizing wave can then propagate in i much
smaller field than the initial field needed. This is because the charges accumulating
on the streamer tip creates an electric field in front of the streamer, increasing the ionization in this region and leading to a propagation of the ionizing wave. A positive
streamer (from a positive charge region) and a negative streamer will propagate differently in the ambient electric field. The processes are illustrated in Figure 3.5 based on
3.2 Thunderstorms and lightning
19
figures from Cooray [2003, Chap. 3.7]. For the positive streamer (a), new avalanches
form in the region in front of the streamer tip. Since the streamer tip is positive, the new
avalanches will be attracted towards the streamer tip. When the avalanches attach to
the streamer tip, the streamer expands. For a negative streamer (b), the new avalanches
that form will be repelled away from the streamer tip. First when the new avalanches
has created enough ionization in front of the streamer tip, the streamer will attach to
the ionized region. In this way the negative streamer propagates in steps and requires
a larger ambient electric field in order to propagate. The electric field required for positive streamer propagation is Est+ ≈440 kV/m, while the negative streamer needs an
electric field of Est− ≈1200 kV/m to propagate [Moss et al., 2006].
+ + + + + + + + + +
- + +
+
-+++++++a)
++ ++ -+-
Streamer
head
------+
++
------+ + +
+ ++
+
----+++
++
+ +-+ -+
+ +--+
++++++
+-+- ++++--+++
+
+++++
+ ++-+ ++++
+- +++
+
++ ++ + +++-++ +
++
+ + ++
+ -+++++
+ +++
+
+++++
- +++++
++ + ++
++ + +
--
---+
----- + ++++
- ++
+ +
-----+
++
-- ++
-----++
+
+
- -- +
-- ++
+
-++
+++- ++
++
++
+
Ea
- - - - - - - - - -
- - - - - - - - - b)
Streamer
head
- - -+ - ++ -- + - -- + -+
- -- - - -+ - + - -- - -+- -+ - ---- -- ++-+ - +- --------- -
+
+++ +
++----------
New
avalanches
Ea
Weak
conducting
channel
Expanding
streamer
+
+
++
+
+
+++ ---+ - - ++
--- +
--- --
+ + + + + + + + + +
Figure 3.5: A schematic drawing of the propagation of positive (a) and negative (b) streamers.
In front of both streamers, small avalanches of electrons form. For the positive streamer,
these avalanches will be attracted towards the streamer tip and the streamer will expand in
an almost constant way. For the negative streamer, the avalanches will be repelled from the
streamer tip. When the avalanches has created enough ionization in front of the streamer tip,
the streamer will jump to this ionized region and thus expand in a step-wise manner. Image
credit: Alexander Skeltved
If the streamer channel gets warm enough or if several streamers heat the area, a
channel with high conductivity will develop. This is called the leader. In the leader,
the conductivity is high enough for electrons to go large distances and more charge can
accumulate in the leader head. Because of the much higher charge of the leader head, a
leader can propagate in even lower ambient fields than the streamers. The propagation
20
Theories of production
of the leader has the same main properties as the streamer, but where the streamers
take the same role as the small avalanches as described in connection to streamers.
An area in front of the leader will have high enough electric field to sustain streamer
propagation and when the streamers create enough conductivity in front, the leader
propagate. Since negative leaders repel the streamers, a negative leader will propagate
in steps, the same way as for streamers. The leader can propagate over large distances
to connect the different charge regions of the clouds and create a breakdown.
3.3 The Thermal runaway theory
The Thermal runaway theory is one of the two main theories of TGF production. Thermal runaway is the process in which thermal electrons are accelerated to relativistic
runaway electrons. This happens when the electric field is higher than the critical electric field Ec as shown in Figure 3.1. As this field is much larger than the classical
breakdown electric field, such electric fields can only exist in a very localized area.
Such an area is shown in models to exist just in front of the streamer tips [Moss et al.,
2006]. Here, the field can get up to at least 32 MV/m, which is slightly higher than Ec
[Moss et al., 2006]. This is illustrated in Figure 3.6. The surface charge on the streamer
tip will create a small region with a very strong electric field.
Ionisation
region
+++++
++ +++
+
+
+
Es
Es
I
l
r
Figure 3.6: An illustration of the tip of the streamer, depicting how the surface charge create
a region of strong electric field at the tip of the streamer. This field can be large enough to
accelerate low energy electrons to keV energies. Image credit: Alexander Skeltved
Celestin and Pasko [2011] showed that this field could accelerate electrons to energies of tens of keVs. As seen from the friction curve in Figure 3.1, the continued
acceleration of the electrons can then be sustained by an electric field on the order of
0.5-1 MV/m. This is on the same order as the electric field needed for the propagation
of streamers and are present in the streamer zone around the leader tip. This is illustrated in Figure 3.7. In the streamer zone, the electric field is larger than 1.2 MV/m
for a negative leader/streamer. The streamer zone has an available potential of up to
300 MV [Mallios et al., 2013] and can hence accelerate the electrons to energies on the
order of what is observed in TGFs. The acceleration and multiplication of electrons
3.4 Feedback
21
through the RREA can continue in the ambient field of the thunderstorm if this field
is larger than Eb . In simulations made by Celestin and Pasko [2011], the streamer and
leader fields seems to be able to produce the required number and energies of initial
electrons without further acceleration and multiplication.
E<Ecr
Streamer
zone
E>Ecr
Ecr
E
Expanding
leader
E
++ +
+ -+
-+ +
+ ++- +
-+ - +
+ -+
+
++
+ ++-
Leader
channel
Figure 3.7: An illustration of the leader tip with the streamer zone. In the streamer zone
electrons of keV energies can accelerate to MeV energies [Mallios et al., 2013]. Image credit:
Alexander Skeltved
This theory then creates the TGFs from thermal electrons already present in the air
and only requires a discharge to develop without any further external input.
Laboratory x-rays and x-rays from the stepping process of lightning, seems to be
produced by thermal runaway. The negative leader will have the most charged accumulated on the tip just before the stepping occur, which corresponds well with the
timing and energies of x-rays observed from lightning Dwyer et al. [2004]. The x-rays
from sparks reported by Kochkin et al. [2012], is shown to occur just before the positive and negative streamers connect. At this time, a large potential is squeezed between
the two streamers, making this a probable timing for the x-rays to occur.
3.4 Feedback
The feedback process was first described in connection to TGFs by Dwyer [2003] and
is a development of the RREA. The high energy electrons produced in a RREA creates
photons via bremsstrahlung. In the photons interaction with the air, some of the photons
go through pair production creating one electron and one positron. If this occurs inside
the electric field, the positron will accelerate in the opposite direction of the electrons.
If this positron collides with an electron further down in the electric field, the electron
can acquire enough energy to become a seed electron, starting a new RREA. This is
known as positron feedback.
The photons created by the bremsstrahlung can also contribute more directly to
the feedback. If the photon is Compton scattered through interaction with the air, it
22
Theories of production
might change direction with more than 90 degrees from the direction of the electrons
creating it. The photon will then travel backwards in the electric field. If the photon
gets absorbed by an electron through photo-absorption, the additional energy acquired
by the electron might be enough to make this a new seed electron. If this happens, a
new RREA can develop. This is known as photon feedback.
Hence the feedback process is a multiplication of RREAs. Generally, the number
of relativistic electrons when the feedback process is included is given as:
1 − γn
Ff b = FRREA
1−γ
(3.4)
where FRREA is the number of relativistic electrons created by a single RREA, n is
the number of avalanches, and γ is the number of new avalanches created by each
avalanche. γ is known as the feedback factor. n is often given as t/τ where t is the time
since the start of the feedback process and τ is the time it takes for one photon/positron
to go around and start a new avalanche. For E > 350 kV/m, τ is found to be less than
10 µ s, and for E > 500 kV/m, τ is less than 3 µ s [Dwyer, 2003].
From equation 3.4, we see that the equation behave very differently for γ <1 than
RREA
for γ >1. For γ <1 the number of electrons will converge to Ff b = F1−
γ when n → ∞.
This means that as long as γ is less than 1, the feedback will add significantly to the
number of electrons, but the process will eventually stop even if the electric field is
always above the field required for RREA.
If γ =1, the equation will give Ff b = nFRREA . This means that the number of electrons will reach a form of steady state where one avalanche create one new avalanche.
As long as the electric field stay above Et h as required for the RREA, the number of
electrons will increase at a constant rate.
γ >1, will lead to an exponential growth of the number of electrons when n → ∞.
The number is given as Ff b = FRREA γ n , where the feedback will quickly dominate the
process.
The value of γ is determined by the strength and size of the electric field. Especially
the photon feedback is increasing significantly with larger horizontal size of the electric field [Dwyer et al., 2012a]. This is due to the probability for Compton shattering
decreasing with angle, making it much more probable that a photon will shatter to an
angle of just over 90 degrees than to shatter to an angle of 180 degrees relative to the
vertical. This means that the probability for this photon to be absorbed by an electron
inside the electric field is much greater when the horizontal size is large.
Figure 3.8 is adapted from Dwyer [2007] and shows a Monte Carlo simulation of
the feedback process in an electric field of 750 MV/m over 150 m (approximately 100
MV potential). The top panel is after 0.5 µ s (∼ 1τ ), the second panel is after 2 µ s and
the lower panel is after 10 µ s. The black lines are electrons (1 line per 1000 electrons)
and the blue lines are positrons. The photons are not drawn on this figure. This shows
how quickly the multiplication increase if the electric field is large enough.
The only thing that will bring the exponential growth of avalanches to an end is
that the electric field is reduced to a level where γ <1. As the avalanches themselves
are representing a current and a lot of low energy photons are produced from ionization
creating an even larger current, the RREA and feedback process will quickly reduce the
electric field back to a stable situation. This discharge of the electric field will produce
3.4 Feedback
23
Figure 3.8: Simulation of the feedback process in an electric field of 750 MV/m over 150 m.
Top panel: t < 0.5 µ s, middle panel: t < 2 µ s, lower panel: t < 10 µ s. Black is electrons (1
per 1000 are drawn) and blue is positrons. Figure adapted from Dwyer [2007].
little or no light as no hot channel is present, and has thus been suggested as a form of
"dark lightning" [Dwyer and Cummer, 2013]. Models indicate that the time it takes for
the feedback process itself to reduce the field so that γ <1 is consistent with the observed
durations of TGFs [Dwyer, 2007]. The fact the process is reducing the field also puts a
limit on the size/strength of the electric field that can exist in the atmosphere over time
[Dwyer, 2003].
The proposed origin of the seed electrons for this process is extensive air showers
of cosmic particles from space.
The feedback process increases the multiplication of electrons so that fewer seed
electrons are required to get the number of photons observed in a TGF. This indicates
that the electric field accelerating the electrons is the ambient electric field of the thundercloud and that the seed electrons can be any seed electrons.
24
Theories of production
Chapter 4
Modeling of TGFs
Direct measurements of the TGFs are hard to acquire, and the production process almost impossible to evaluate without models. The main aim of the models is to use
known physical processes to get the same TGF signals as we observe. Because so many
different processes are involved and because of the large number of elements to model,
most models are only addressing a small part of the full process. Dwyer [2007] has put
together many of the elements to a full simulation where the acceleration of electrons
are through feedback process. In my work I have used a model for photon transport in
air, this model has made us able to understand several features of the TGF observations
that are caused by the photon transport through air. This chapter start with the basics of
this model, before addressing why the bremsstrahlung process is so important to model
correctly and the challenges in doing so. The development of a bremsstrahlung model
suitable for TGF modeling is work in progress, and will hopefully give useful insight
into TGFs.
4.1 Photon transport in air
High energy photons in the air gets attenuated but three main processes: photoelectric
absorption, Compton scattering and pair production. Figure 4.1 is a plot of the interaction cross sections for the three processes including the total attenuation cross section.
The attenuation is dominated by the photoelectric absorption at low energies, by the
pair production at high energies and by Compton scattering at intermediate energies.
In photoelectric absorption the photon energy in absorbed by the atoms of the air. In
Compton scattering, the photon is experiencing what can be seen as an elastic collision
with the atoms. The photon loose some energy to the atom and is continuing with a
lower energy and in a different direction. In pair production, the energy of the photon
creates one electron and one positron in the interaction with air. The excess energy after
the production of the two particles is conserved as kinetic energy of the two particles.
The positron will eventually interact with another electron and annihilate.
Our code is a Monte Carlo (MC) code, and is described in Østgaard et al. [2008]. A
MC code use the probability function for a process to determine if an interaction occur.
In our code, we use the attenuation cross sections presented in Figure 4.1 and evaluate
the probability in length steps along the photon path. If photoelectric absorption occur,
the photon is removed from the simulation. If Compton scattering occur, another MC
evaluation is performed to determine the new energy and direction. The new direction
26
Modeling of TGFs
Figure 4.1: Attenuation cross sections for high energy photons in air. At low energies the
photoelectric absorption is dominating, at high energies the pair production is dominating and
at intermediate energies the attenuation is dominated by the Compton scattering.
of the photon is highly dependent on the energy transferred to the electron. A small
energy loss, generally give a small change in direction, while a large energy loss might
give a large change in direction. If pair production occur, the photon is removed from
the simulation and replaced by a 511 keV photon, representing the energy released
by the annihilation of the positron. The positron is assumed to annihilate at the same
position as the pair production and with no time delay. The code was shown to be
in good correspondence with results from the GEANT3 package, that is a much used
simulation tool developed for high energy physics [Østgaard et al., 2008].
The cross section for attenuation is decreasing with the atmospheric decrees in density at higher altitudes. In the MC-code the attenuation is set to 0 for altitudes above
100 km. This means that when modeling the expected signal at a space craft, no interactions occur above 100 km and the photon will continue with the same direction and
energy. This means that from 100 km altitude the photon density will decrease with
1/r2 , where r is the radial distance.
The input to the model is between 105 and 107 photons with a position, energy
and direction distribution. In paper 2 of this thesis, the energy distribution was kept
constant at a 1/energy distribution for all simulations. This is the hardest spectrum
that the bremsstrahlung process can produce. Both the directional distributions and
the initial positions of the photons was changed between simulations and caused very
different results. This is described more in section 5 and in paper 2.
4.2 The bremsstrahlung process
The bremsstrahlung process is a very important process in the production of TGFs. In
this process, energy from decelerating electrons are emitted as photons. It is the elementary process where the energy from the electric field ultimately end up as gamma
rays and TGFs, and for both the suggested theories it is important to describe the process correctly. It is important that the models are able to get both the energy of the
photons and electrons right, as well as the direction of the photon and outgoing electron. If the energy and direction of photons are not correct, the input to the modeling of
4.2 The bremsstrahlung process
27
photon transport will be wrong. If the electron energies and direction is not right, further acceleration of the secondary electrons will be wrong. To get the bremsstrahlung
process modeled correctly is also important to establish how many high energy photons
each high energy electron produce. This will make us able to more accurately estimate
the number of high energy electrons that are needed to produce a TGF. This is further
described in section 5.7.
Bremsstrahlung is a quantum-mechanical process where an electron interacts with
the electric field of a nucleus or another electron. The incoming electron is decelerated
and loose energy, and the excess energy is emitted as light. The situation is illustrated in
Figure 4.2.For relativistic energies, the process is fully described by the Dirac equation
(the relativistic wave equation), and the differential cross section (number of interactions per unit time per unit flux of incident particles) is expressed as:
d 3σ
α ε1 ε2 p2 k
=
|M|2
4
dk dΩk dΩ p2 (2π )
p1
(4.1)
in units of m = c = h̄ = 1. Here, α ≈ 1/137 is the fine structure constant, k is the energy
of the photon produced in the process, Ω is the solid angle, p1 and p2 is the momentum of the incoming and outgoing electrons respectively, and ε1 and ε2 is the energy of
the incoming and outgoing electrons. |M| is the matrix element for the electron transition 1→2 of the Hamiltonian of the electron in the interaction of a radiation field.
This matrix element depends on the two wave functions of the incoming and outgoing electrons, the distance the electron pass from the charge, the polarization vector,
and the Pauli spin matrix [Haug and Nakel, 2004]. Also, note that the directions of
the photon and the outgoing electron is not restricted by the kinematics as the nucleus
can take any recoil momentum even if the received energy is usually neglectable [Haug
and Nakel, 2004]. This makes the cross section a triple differential over the photon energy, the photon direction and the direction of the outgoing electron. When including
the incoming electron energy, it becomes a quadruple differential.
p1
k
q
p2
Figure 4.2: An illustration of the bremsstrahlung process. An electron with momentum p1
is decelerated in the Coulomb field of a nucleus and exit the field with momentum p2 . The
nucleus receives the momentum q in the process and the energy lost by the electron is emitted
as a photon with energy and direction k.
This equation is not possible to solve in a closed form and one or more assumptions
has to be made in order to solve the equation.
4.2.1 The Born approximation
The most common assumption is the Born approximation. When applying this approximation one includes only the interaction between the wave function of the incoming
28
Modeling of TGFs
electron and the nuclear field of the particle [Nakel, 1994]. For a first order perturbation
in a Coulomb field this results in the Bethe-Heitler formula:
α Z 2 r02 p2
d 3 σb
=
dk dΩk dΩ p2
π 2 kp1 q4
{(
)2
2ε2
2ε1
p1 × k −
p2 × k
D1
D2
(
)
}
p2 × k 2
2k2
2 p1 × k
2
−q
−
+
(q × k)
(4.2)
D1
D2
D1 D2
where Z is the atomic number of the target nucleus, D1 = 2(ε1 k − p1 · k, D2 = 2(ε2 k −
p2 · k and q is the recoil momentum.
The Born approximation is valid for αβZ ≪ 1 and αβZ ≪ 1, where β1 and β2 are the
1
2
velocities of the incoming and outgoing electrons in units of the light velocity [Haug
and Nakel, 2004]. This condition is satisfied for low atomic numbers, and as long as
both the incoming and outgoing electrons are relativistic. However, the condition is not
satisfied at the short wave limit where almost all the energy of the electron is transferred
into the photon and the energy of the outgoing electron get close to 0. From equation
4.2, we see that the cross section goes to 0 as p2 → 0 when using the Born approximation. But the exact point-Coulomb wave function included in the Dirac equation is
−1/2
not finite and diverges as p2
as p2 → 0, leading to a finite cross section [Haug and
Nakel, 2004]. A correction factor, named the Elwert factor, was introduced by Elwert
[1939]:
a2 1 − exp(−2π a1 )
FE =
(4.3)
a1 1 − exp(−2π a2
where a1 = αβZ and a2 = αβZ . On the short wave limit, where p1 ≈ p2 , FE ≈1, while the
1
2
factor a2 compensate for p2 when p2 → 0.
Commonly other correction factors are added to the Bethe-Heitler formula to account for the screening by the electrons around the nucleus Haug and Nakel [2004];
Koch and Motz [1959].
Both the screening and the ad-hoc solution to the problem with the high energy limit
are important factors for TGF modeling. Especially the problems at high energies. If
the cross section used in models are too low at the high energy limit, the model will
suggest that TGFs require more high energy electrons that what is true. If the cross
section is too high, the model will give too few high energy electrons. As this numbers
are important to differentiate between the two theories, more focus should be put on
the bremsstrahlung modeling.
4.2.2 The Sommerfelt-Maue wave function
Another approach to solve the Dirac equation is the Sommerfelt-Maue wave function
Elwert and Haug [1969]. This allows for applying more than one of the Matrix elements of equation 4.1 [Roche et al., 1972], and is valid at all energies for low atomic
numbers where α Z ≪ 1 [Haug, 2008]. Haug [2008], brought this one step further by
including the full screening. As the Coulomb and the screening is independent of each
other and hence additive Olsen et al. [1957], the true screened cross section can be
4.2 The bremsstrahlung process
29
written as:
(
d 2σ
dk dΩk
)screened
exact
(
d 2σ
≈
dk dΩk
)unscreened [( 2 )screened ( 2 )unscreened ]
d σ
d σ
+
−
dk dΩk Born
dk dΩk Born
exact
(4.4)
where the unscreened, exact cross section is the cross section from Roche et al. [1972],
the Born approximated cross sections are from Fronsdal and Uberall [1958]. The same
additive property is valid for d σ /dk [Haug, 2008].
Haug [2008] give the full triple cross section, which is possible to integrate numerically. For TGF research, this will be a much more accurate approach, avoiding the
problems at the high energy limit. To do an implementation of this, to use for TGF
modeling is work in progress and will hopefully give interesting and important results.
4.2.3 Use in models
Seltzer and Berger [1985] and Seltzer and Berger [1986] used many of the available
formulas at the time and made a big matrix of cross sections. The cross sections that
are valid for different energies and atomic numbers were calculated and an interpolation was made where no formulas were valid. For relativistic energies and low atomic
numbers, they used the Davies, Bethe, Maximon and Olsen (DBMO) function, the
Bethe-Heitler and other formulas, all using the Born approximation, and included the
short wave limit corrections by Elwert [1939] and several screening corrections.
Dwyer [2007] made a full simulation of the TGF process. To calculate the
bremsstrahlung cross sections, he used a standard Born approximation with a form
function to account for screening and a high energy limit correction. Lehtinen et al.
[1996] also used the Born approximation to calculate the bremsstrahlung in his Monte
Carlo simulation.
Both the Bethe-Heitler and the Sommerfelt-Maue wave functions are triple differential equations and are assuming that no energy is transferred to the nucleus. It is
differentiated in photon energy, direction of photon and direction of outgoing electron.
The double and single differentials are usually found by numerical integration. Köhn
and Ebert [2014] found an analytical expression for the double and single differential
of the Bethe-Heitler equation. Seltzer and Berger [1985] only give the single differential and in a model their matrix will have to be differentiated twice to acquire the
electron and photon direction after interaction.
30
Modeling of TGFs
Chapter 5
Source properties of TGFs
Ever since the first discovery of TGFs, establishing the source properties of TGFs has
been one of the basic questions. Some constraints on the properties are established, but
to confine it even further is limited by the number of measurements. One problem is that
changes in several different properties might give the same expected measurement. For
instance, the seemingly wide beam configuration showing in the accumulated RHESSI
spectrum, might equally well be a result of an accumulation of beamed TGFs with different initial angle to the vertical. To establish the initial properties are very important
in order to constrain the production theories. In the streamer/leader theory, every lightning should be producing a TGF even if some of the TGFs are too weak to reach our
satellites in space. According to the feedback theory, only the thunderstorms with the
highest electric fields are producing TGFs. This means that establishing the ratio of
TGF to lighting might differentiate between the two theories.
The three papers included in this thesis are all addressing the source properties of
the TGFs. Paper 1, looks at how the fluence distribution is at satellite altitude and
use this to address the question on the ratio of TGF to lightning. Paper 2 estimate the
number of photons in a average RHESSI TGF and use this to look at how balloons and
aircraft observations can be utilized to constrain the source properties further. Paper
3, is a development of paper 1. This paper look at how the fluence distribution at the
source is different from the fluence distribution at satellite altitude.
In this chapter I present the known constraints on the source properties of TGFs.
At the end of the chapter I will also discuss how the determination of the initial source
properties affect the theories presented in chapter 3.
5.1 Space and time distributions
5.1.1 Geographical distribution
Already in the first report on TGFs by Fishman et al. [1994], the close similarity between the geographical distributions of lightning and of TGFs were noted. Later observations from RHESSI, AGILE and Fermi have all confirmed this Briggs et al. [2013];
Fuschino et al. [2011]; Gjesteland et al. [2012]; Smith et al. [2005]. This means that
most lightning happen over land or coastal areas where the convective energy is high
and thunderstorms more easily develop. Figure 5.1 is adapted from Splitt et al. [2010]
and shows the location of the satellite nadir for TGFs between 2002 and 2007 from the
32
Source properties of TGFs
first RHESSI catalog by Grefenstette et al. [2008]. The figure depicts the coastal areas
in gray, coastal areas are defined as areas within 370 km from any shoreline.
Figure 5.1: The position of RHESSI nadir at the time of TGFs. The gray areas are the areas
within 370 km from the coast. It can be seen that most TGFs occur over land or coastal areas.
The figure is adapted from Splitt et al. [2010].
When using WWLLN to geolocate the lightning that are the probable source of
the TGF, it is also clear that the source lightning is often shifted towards coastal areas
relative to the satellite nadir especially in America and Asia [Briggs et al., 2013; Nisi
et al., 2014]. This is shown in Figure 5.2, which is adapted from Briggs et al. [2013].
The figure shows the WWLLN located spheric of the probable TGF source lightning
as circles and the start of the lines mark the location of Fermi nadir.
5.1.2 Distance from satellite nadir
Due to BATSEs ability to determine the direction of the TGFs, the position of these
events could be found directly. With all the other instruments, another method is required to locate the source. The method mainly used is to locate the lightning most
closely connected in time and space using VLF or HF wave signals from lightning.
As the VLF networks have a low detection rate (<10 % globally [Abarca et al., 2010;
Collier et al., 2011; Connaughton et al., 2010]) and the satellite spend very little time
above HF networks, only about 20-35 % of TGFs have connected geolocated lightnings
[Briggs et al., 2013; Collier et al., 2011]. Where the geolocated lightning or position
of TGF source is available, the distance from the source is usually within 300 km of
the satellite nadir, but with some out to a distance of 8-900 km [Briggs et al., 2013;
Collier et al., 2011; Fishman et al., 1994; Hazelton et al., 2009; Nisi et al., 2014]. Figure 5.3 show the distance between the RHESSI nadir and the geolocated lightning from
WWLLN for the second RHESSI catalog for the years 2002-2011. The set consists
of a total of 265 TGFs and the figure is adapted from Nisi et al. [2014]. The figure
shows that the density of source lightning is largest close to the satellite nadir. This
is as expected, as the TGFs originating from larger distances go through more air and
5.1 Space and time distributions
33
Figure 5.2: The location of the Fermi nadir and the probable source lightning show that most
TGFs are originating from coastal regions even if the satellite is inland or above the ocean.
The circles marks the location of the source lightning and the start of the line marks the Fermi
nadir. The blue circles are TGFs found from the continuous data collection and the red circles
are triggered TGFs. The figure is adapted from Briggs et al. [2013].
are hence more attenuated. The intensity of the TGFs are also reduced by the 1/R2
effect, and hence a larger portion of the TGFs from larger distances will fall under
the detection threshold of the instrument. The greater loss of intensity for TGFs from
large distances is the main reason for doing the distance correction of the fluence when
searching for the initial source fluence that is the main purpose of paper 3 of this thesis. Briggs et al. [2013] argue that the density is almost constant out to a distance of
300 km from nadir before falling off. In Figure 5.3 we can not see any such effect.
5.1.3 Annual and diurnal distributions
The annual and diurnal TGF distributions also follow the lightning distributions closely.
Most TGFs occur in the summer and early fall season and in the afternoon local solar
time [Splitt et al., 2010]. It is the available convection energy that are the main driver
of these variations. In summer and early fall and in the afternoon, the sun has been
heating the surface to a level where the thunderstorms are more likely to occur. Figure
5.4 shows the diurnal pattern of the first RHESSI catalog TGFs and lightning rates from
LIS/OTD. The boxes are the lightning measurements, the black columns are the oceanic
TGFs, the dark gray columns are the TGFs from inland regions and the light gray
columns are for the combination of land and coastal TGFs. It is clear that the diurnal
distribution of TGFs follows about the same pattern as the lightning. The oceanic TGFs
looks like they might follow a different distribution, but the number of events are small
(39 events). The figure is adapted from Splitt et al. [2010].
5.1.4 Duration of TGFs
Table 5.1.4, list the TGF duration as determined from satellite data.
The first TGFs from BATSE had a mean duration of around 2 ms [Nemiroff et al.,
1997]. It was also noticed that the TGFs from further distances had longer durations.
34
Source properties of TGFs
Figure 5.3: The distance between the RHESSI nadir at the time of TGFs and the geolocated
lightning from WWLLN for the years 2002-2011. As can be seen the source density is largest
close to the satellite nadir. This is as expected as farther distances and more atmosphere
between the location of TGF production and the satellite makes more TGFs fall below the
detectability threshold of the instrument.
Satellite
BATSE
Fermi trigger
Fermi continuous
RHESSI
Mean duration
2 ms
0.1 ms
0.3 ms
0.3 ms
Duration definition
Subjectively from light curve
t5 0
t9 0
2σ Gaussian
Reference
Nemiroff et al. [1997]
Fishman et al. [2011]
Briggs et al. [2013]
Table 5.1: The duration of TGFs as measured by different satellites. Note that the definition
of duration is different between different papers. The duration is highly dependent on the
trigger/selection criteria of the TGFs.
This was found to be due to the Compton scattered photons arriving later than the initial
photons, prolonging the measurements of the TGF [Celestin and Pasko, 2012; Feng
et al., 2002; Grefenstette et al., 2008; Østgaard et al., 2008]. In subsequent satellite
experiments, the duration of TGFs are found to be significantly shorter. This is mainly
due to the trigger or selection criteria for TGFs at the different instruments. Since
BATSE is having a trigger time of 64 ms, only long and powerful TGFs will produce a
significant signal relative to the background. For RHESSI and Fermi where all the data
are downloaded, using shorter search bin widths makes one able to find shorter events.
In the second RHESSI catalog, the mean duration of TGFs (2 σ Gaussian) is around
0.3 ms. The mean duration (t90 value) for Fermi events is also around 0.3 ms [Briggs
et al., 2013]. In the search of the RHESSI data set, all events shorter than 0.1 ms is left
out due to the high probability of this being a cosmic ray [Gjesteland et al., 2012]. In
the Fermi data, Briggs et al. [2013] notes that the shorter events are highly affected by
dead time. Both these indicate that the actual mean duration might be shorter.
The production process of TGFs is creating a large number of high energy photons
in a short period of time, making the number of photons and the duration important in
5.1 Space and time distributions
35
Figure 5.4: The diurnal distribution of TGFs from the first RHESSI catalog and the lightning
density from LIS/OTD. The boxes indicate the lightning density, the black is oceanic TGFs,
the dark gray is inland TGFs and the light gray is the combined land and coastal TGFs. It is
clear that at least the land and coastal TGFs follow the same diurnal distribution as lightning.
The figure is adapted from Splitt et al. [2010].
order to establish the production theory. As noted for the BATSE TGFs, the observed
duration for TGFs at large distances will be elongated compared to the actual duration.
Also the ability of the instrument to detect short events creates an uncertainty about the
actual duration of a TGF.
5.1.5 Timing of TGFs
The TGF duration is on the order of 0.1 ms, while the duration of lightning is of the order of 100 ms. Thus, determining when during the lightning process a TGF occur will
be important in order to develop the production theories further. The RHESSI instrument, that have been most extensively used, have a problem with the timing [Grefenstette et al., 2008]. From a cosmic gamma ray burst, this error was estimated to be
around 2 ms [Grefenstette et al., 2008], but whether this error is constant or varying
with time is not known. The results from Collier et al. [2011] indicate a systematic error. Nevertheless, Lu et al. [2010] and Cummer et al. [2011] was able to establish that
the TGF is produced in the initial phase of the lightning. Østgaard et al. [2013] found
one RHESSI TGF over lake Maracaibo with simultaneous optical measurements from
LIS and VLF signals from both WWLLN and the network in Duke. They concluded
that the TGF were originating from an IC lightning and from the beginning of the lightning flash. As was discussed in section 2.2.3, one should be careful when assigning a
VLF signal to the lightning as it might be the TGF electrons that are creating the signal [Connaughton et al., 2013; Østgaard et al., 2013]. In this respect, the result from
Østgaard et al. [2013] is a much stronger result.
36
Source properties of TGFs
5.2 Number of TGFs
5.2.1 TGF/lightning
It is still not known if all lightning produce TGFs or if only a specific type of lightning
create TGFs. Also, if only some lightning produce TGFs what are the special properties these lightnings have in order for those lightnings only to produce TGFs. Cummer
[2005] was one of the first to connect TGFs to a specific type of lightning. Using a network of VLF receivers at Duke University they found 26 TGFs that were all connected
to positive IC lightning (intra-cloud lightning transporting negative charges upwards).
Later, the same has been reported by several studies [Lu et al., 2010; Østgaard et al.,
2013; Shao et al., 2010; Stanley et al., 2006]. The reason for the observed TGFs to
be connected to +IC lightning might be an effect of the altitude of IC lightning being
high compared to CG lightning, making only the TGFs from IC lightning reach space.
This in combination with the positive polarity creating TGFs upwards while the negative lighting produce TGFs downwards (in the direction of the transport of negative
charges), making only the TGFs from positive IC lightning visible from space. That
means that these studies do not exclude the possibility of TGFs being produced in all
lightning, as there might exist TGFs that are not possible to observe from space either
because they are to weak or because of the TGF developing in the wrong direction.
The observed TGF/lightning ratio is seen to change in both space and time. Figure
5.5 show how the TGF/lightning ratio change geographically based on LIS lightning
and RHESSI TGFs. 0 is the median ratio, blue colors is a smaller than median ratio,
red is higher than median ratio. The figure has taking into account the changes in
tropopause altitude (transmission of gamma rays) in time and location. The figure is
fully described in Nisi et al. [2014] (Paper 3 of this thesis). It is clear from the figure
that the ratio is significantly smaller in Africa than in Asia and America. The same
geographical difference is also found in Briggs et al. [2013], using the Fermi TGF
measurements. The explanation for the differences is not yet known.
Figure 5.5: This map is showing how the TGF/lightning ratio, based on RHESSI TGFs, is
changing geographically relative to the median ratio. 0 is median ratio, blue is a lower than
median TGF/lightning ratio, red is a higher than median ratio. It can be seen that the ratio is
significantly higher in America and Asia than in Africa. The full description of the figure can
be found in Nisi et al. [2014](Paper 3 of this thesis)
Splitt et al. [2010] show that the TGF/lightning ratio has a diurnal dependence as
well. Just after midnight local solar time the ratio can be about 30% higher than average
and around mid day the ratio can be as small as 50% less than average.
5.2 Number of TGFs
37
The ratio are probably also having an annual dependence as the tropopause has
an annual dependence and thunderstorm tops are mainly following the altitude of the
tropopause. In the subtropics and higher latitudes the annual variability is mainly due
to the difference in sunlight in summer and winter. The tropopause in the tropics are
generally not changing much with latitude or hemisphere, but the tropopause pressure
is shown to have an annual pattern with higher pressures in June, July and August (JJA)
than in December, January and February (DJF) [Reid and Gage, 1996]. This variation
is due to a stronger Brewer-Dobson circulation in the north subtropics winter (DJF)
than in the south subtropics winter (JJA), due to more land masses in the north and the
topography of these land masses [Fueglistaler et al., 2009]. Since lightning and TGFs
mainly occur in local summer, this means that most TGFs in the north will occur in
the months when the tropopause pressure is high (JJA), and the TGFs in the south will
occur when the tropopause pressure is lower (DJF). The tropopause pressure for the
time and place of TGFs is shown in Figure 5.6, which demonstrates that the tropopause
pressure for TGFs in JJA is 10-15 hPa higher than in DJF between -20 and 20 degrees latitude. Lower tropopause pressure indicate higher altitudes, with a difference
of around 25 hPa being about 1 km altitude difference at these heights. The method
used for finding the tropopause altitude is described in Paper 3. These results means
that we can expect the measured TGF-to-lightning ratio to be smaller in summer (JJA)
than in winter (DJF), due to an easier escape of the gamma rays from the atmosphere
during December, January and February.
Figure 5.6: Latitudinal difference in tropopause pressure for TGFs occurring in June-JulyAugust and in December-January-February. The lower pressure in DJF is due to a stronger
Dobson-Brewer circulation in these months. Figure is from Nisi et al. [2014].
The ratio detected by instruments are of course also depending on properties like
energy threshold and efficiency of the instrument. Based on the RHESSI data, Østgaard et al. [2012] found the average ratio of RHESSI TGFs/lightning to be 1 × 10−4 .
Briggs et al. [2013] found the average Fermi TGF/lightning ratio to be 3.8 × 10−4 . The
38
Source properties of TGFs
differences can be explained by differences in instrumentation and search methods.
5.2.2 Total global number of TGFs
The total number of TGFs is also not straight forward as no-one knows how the fluence
distribution looks at below the threshold for detection of the instruments. Figure 5.7 is
adapted from Gjesteland et al. [2012] and shows how the new search algorithm used in
the second RHESSI catalog expanded the fluence distribution to lower numbers. The
red curve shows the first catalog TGFs and the black curve shows the second catalog,
but what happens at even lower fluences?
Figure 5.7: Fluence distribution of the first (red) and second (black) RHESSI catalog TGFs.
As the new catalog expands the distribution to lower fluences, it is clear that we might just see
the tip of the iceberg and are limited by the detection threshold of the instrument. Figure is
adapted from Gjesteland et al. [2012].
If the distribution has a sharp cut off at the low end it means that even with better
detectors, we will not detect more TGFs. If there is no such cut of, it means that there
are a lot of TGFs below the detection threshold. Somewhere in between would be a
roll off. If there is a sharp cut off at low fluences that means that there must be a sharp
lower limit to the number of photons/electrons that can exist in a TGF, this will be
further discussed in section 5.6
Another question is how quickly the number of events increase with decreasing
fluence. If there is a slow increase, we are seeing a larger portion of the TGFs than
if there is a large increase. Figure 5.8 shows the fluence distribution as measured by
RHESSI in gray and the dead-time corrected fluence distribution in black. If the fitted
power laws were expanded to lower fluences, we would expect a lower number of new
events with the dead-time corrected distribution than with the measured distribution.
On the basis of the instrument detection threshold, several numbers are presented
in literature. These are summarized in table 5.2.2. Carlson et al. [2009] and Smith
et al. [2010] both used the RHESSI measurements, but different methods to estimate
the total number of events.
5.2 Number of TGFs
39
Figure 5.8: The measured fluence distribution go the second RHESSI catalog (gray) and the
dead-time corrected fluence distribution (black). If the power law shown in the figure is expanded to lower fluxes it is clear that a larger number of events would be expected from the soft
(gray) distribution than the hard (black) distribution. Figure is from Østgaard et al. [2012](Paper 1 of this thesis).
Satellite
RHESSI
RHESSI
AGILE
Fermi
RHESSI and ADELE
RHESSI, Fermi and ADELE
Number of TGFs per year
2 × 104
≥ 5 × 105
8 × 104 -2 × 105
4 × 105
5 × 106
2 × 107
Reference
Smith et al. [2010]
Carlson et al. [2009]
Fuschino et al. [2011]
Briggs et al. [2013]
Smith et al. [2011b]
Østgaard et al. [2012]
Table 5.2: Estimated global number of TGFs above the detection threshold and within the orbit
of the instruments as presented in the literature.
The ADELE airborne instrument has a significantly lower threshold than the other
instruments, but with very limited time in the air and only one TGF observation the
numbers will have a large uncertainty. Based on the low number of detected TGFs
Smith et al. [2011a] concluded that TGFs are a much more rare event than previously
thought. The assumptions made to reach this conclusion was partly questioned by
Hansen et al. [2013] and Østgaard et al. [2012], and is discussed in Paper 2 of this
thesis. Using the one detection and the non-detection of ADELE, Smith et al. [2011b]
find a number of 5 × 106 TGFs per year with an error estimate of up to an order of
magnitude. Østgaard et al. [2012] (Paper 1 of this thesis) used both RHESSI and
Fermi in addition to ADELE. They used the fluence distribution of both RHESSI and
Fermi (corrected for orbit and efficiency to be comparable) and the low detection rate
of ADELE. They argued that the fluence distributions has a roll off at low fluences
and also that it is a reasonable probability of ADELE not detecting more TGFs. Using
this they concluded that the global number of TGFs within +/- 38 degrees latitude and
above 5/600 of the RHESSI threshold would be at least 2 × 107 , and that the possibility
of all lightning producing TGFs could not be ruled out.
40
Source properties of TGFs
5.2.3 x-ray/spark
If TGFs are produced by the thermal runaway, x-rays from sparks and lightning might
be a low flux and low energy TGF. This has encouraged the search for x-rays in sparks.
In different experiments by Dwyer et al. [2005], Dwyer et al. [2008] and Kochkin et al.
[2012], up to 70 % of the sparks have been seen to produce x-rays, with no observable
difference between x-ray producing sparks and non-producing sparks. The question is
if all sparks actually produce x-rays, but that the x-rays are highly directional. If so,
the reason for the non-detection will be that the detectors were outside of the region of
x-rays. With production through thermal runaway this is not unthinkable. In Eindhoven
in January 2013 we set up several detectors in different configurations around a spark
generator and produced more than 1000 sparks. The analysis of these sparks is ongoing,
and the aim is to look for directionality of the x-rays. Photo...?
5.3 Energy
The first observations from BATSE suggested that the phenomenon was energetic, but
all photons with energies larger than 300 keV was stored in one energy channel and
it was not possible to figure out how high energies that could be present in the TGFs
[Fishman et al., 1994]. The data from the RHESSI satellite confirmed the high energies
and found photons with energies of at least 20 MeV [Smith et al., 2005]. Recently both
AGILE and Fermi has been able to expand this to single photon energies of at least 40
MeV being present in TGFs [Marisaldi et al., 2010b; Tierney et al., 2013].
Both AGILE and RHESSI detect around 10-30 photons in a typical event and to do
spectral analysis, the TGFs have to be superposed. The TGFs measured by BATSE and
Fermi generally contains enough photons to do spectral analysis on individual TGFs.
The spectral analysis provided the first indications on the altitude and emission angle
distribution of TGFs.
5.4 Altitude distribution
The production altitude of individual TGFs and the altitude distribution of the set of
TGFs are important parameters that can develop the production theories further.
The first proposed altitude for TGFs was production above 40 km and based on the
recognition that low energy photons do not travel far in the Earths atmosphere [Fishman
et al., 1994]. As the TGFs contained many photons with energies smaller than 60 keV,
Smith et al. [2005] concluded with a production altitude of more than 25 km. This did
not take into account that the low energy photons could have been produced at higher
altitudes from Compton scattered electrons or that the photons had lost energy through
Compton scattering at higher altitudes. When all the important processes for photon
interaction in air was included in models, the spectral shape was the main indication
of altitude. The spectral analysis of the combined RHESSI spectrum also indicated an
initial altitude of less than 20 km [Babich et al., 2008; Carlson et al., 2007; Dwyer
and Smith, 2005; Gjesteland et al., 2011; Hazelton et al., 2009]. The first spectral
analysis of the BATSE data, showed signs of two altitude regions, one around 40 km
and one below 20 km [Østgaard et al., 2008]. After Grefenstette et al. [2008] pointed
5.4 Altitude distribution
41
out significant dead time problems with the BATSE instrument, Gjesteland et al. [2010]
revisited the BATSE data and concluded that all TGFs seemed to originate at altitudes
consistent with thunderstorm altitudes. One problem with this method of comparing
spectra is that the initial direction of the photons also change the spectra. This will be
discussed below. Another problem is that the differences between 20 km and lower
altitudes are small.
Another approach used to derive the initial altitude is to look at the lightning itself
with HF and VHF detectors. To do this the TGF producing lightning have to occur
within a network of HF receivers. Triangulations of the signals in the receivers can
give the position and altitude of the lightning. Stanley et al. [2006] were the first to
do so. They analyzed 5 lightnings connected to RHESSI TGFs and found altitudes of
11.5-13.6 km. Later, Lu et al. [2010] and Shao et al. [2010] did analysis for 1 and 9
TGFs and found altitudes of 10-11 km and 10.5-14.1 km respectively.
As the TGFs are now determined to originate inside the thunderstorms, the
tropopause becomes an important limit. The tropopause is the located between the troposphere and the stratosphere and is the upper boundary for most clouds. Some clouds
with exceptionally strong updraft might overshoot the tropopause. Liu and Zipser
[2005] investigated cloud tops found from micro wave measurements made with an
instrument on-board the TRMM satellite. During 5 years between 1998 and 2003 they
found about 9000 clouds that were overshooting the tropopause as defined by NCEP/NCAR. In the same years, LIS (also on-board the TRMM satellite) measured around 1.2
million thunderstorms. This means that around 0.8 % of all thunderstorms within +/35 degrees latitude has overshooting clouds.
The tropopause is highest in the tropics, with a maximum of about 16 km, becoming
lower at higher latitudes where it can be as low as around 8 km. For a given location,
the annual mean usually differs up to 0.5 km between years, while the monthly mean
varies around 1 km over a year [Seidel and Randel, 2006]. The day-to-day variability
for a given location has a mean of 45 hPa or 1.4 km, but can be as much as 2 km
[Das et al., 2008; Seidel and Randel, 2006]. This gives a big variability in the expected
maximum altitude of the TGFs.
Another important property to consider is how the photons in one TGF is distributed
in altitude. Smith et al. [2011a] used the RREA simulations from Dwyer [2007] with
a constant sea equivalent electric field of 400 kV/m over an atmospheric depth of 87
g/cm2 of air. To use atmospheric depth as a measure of size of the electric field implies
that the avalanche region at low altitudes are more compressed than at high altitudes.
At an altitude of 8 km, 87 g/cm2 corresponds to a vertical distance of 1500 m, while at
20 km it corresponds to 5800 m [Hansen et al., 2013]. Figure 5.9 is adapted from Smith
et al. [2011a] and shows the photon altitude distribution for a production altitude of 12
km. The figure reveals that most of the photons are produced close to the upper limit of
the electric field. Especially for observations at low altitudes with for instance aircrafts
or balloons the photons crated at the bottom of the electric field makes a significant
difference. This is further discussed in Hansen et al. [2013], which is Paper 2 of this
thesis.
42
Source properties of TGFs
Figure 5.9: The photon altitude distribution for a TGF for an initial production altitude of 12
km. The electric field is stretching over an atmospheric depth of 87 g/cm2 which corresponds
to around 9.7-12 km at this altitudes. The figure is adapted from Smith et al. [2011a]
5.5 Emission angles of TGF photons
The spectral shape of the measured TGFs give some clue to the emission angles of
the TGF photons. One of the main problems is that the spectral shape change with
both emission and observational angle. Figure 5.10, is adapted from Gjesteland et al.
[2011] and shows how the fluence change with the two angles, as calculated from the
Monte Carlo model of photon transport presented in section 4.1. Figure 5.10 a) show
the two angles, the observation angle is α and the emission angle is θ . In b) is shown
the simulation results. The solid line is if the photons were emitted in all directions and
not attenuated by the air. In this case, the reduced intensity would only be due to the
reduction with distance. The dash-dotted line is for an emission angle of 60 degrees,
the dashed is 40 degrees emission angle and the dotted is for a 20 degree emission
angle.
Outside of the emission cone, the only photons measured will be either Compton
scattered photons or photons produced by annihilating positrons. As these photons
will be reduced in energy from the original energy, the spectrum is expected to be significantly softer for these photons. By comparing modeling results with the measured
spectrum from around 100 RHESSI TGFs, Gjesteland et al. [2011] found that the probable emission cone is a broad beam of with at least 40 degrees half angle. This result
compared well with previous results from Carlson et al. [2007], Østgaard et al. [2008],
Hazelton et al. [2009] and Gjesteland et al. [2010].
5.6 Number of initial photons
a)
43
b)
Figure 5.10: Modeling results of how the angle of observation and the half angle of the emission cone affects the fluence observed at a satellite. a) shows an illustration of the setup, α is
the observation angle and θ is the half angle of the emission cone. b) shows the number as
a function of the observational angle. The source altitude is put at 15 km. The solid curve is
showing how the number change if only considering the reduction in fluence with distance.
The dashed-dotted curve is for 60 degrees emission angle, the dashed curve for 40 degrees
emission half angle and the dotted curve for 20 degrees emission half angle. It is clear that the
number of photons drop significantly (but not to 0) outside the emission cone. All the photons outside the cone is either produced by annihilated positrons or they are Compton scattered
away from their initial direction. The figure is adapted from Gjesteland et al. [2011]
The uncertainty is large in these results. For all the results based on RHESSI measurements, the spectrum used is a cumulative spectrum. This means that the wide beam
might be as a result of the tilt of the beam and not only by the width of the emission
cone. Another issue is that the altitude of the production is not established.
5.6 Number of initial photons
The number of initial photons was first estimated by Dwyer and Smith [2005], who
concluded with a number of about 1016 photons above 1 MeV for a source altitude
of 21 km and 2 × 1017 for a source altitude of 15 km. The number of 1017 has subsequently been extensively used. The number of photons in a TGF was also estimated and
discussed in Hansen et al. [2013] (Paper 2 of this dissertation), by using the RHESSI
average. The loss of photons in the atmosphere was estimated using the Monte Carlo
model of photon transport described in section 4.1, and the number subsequently estimated from basic geometry. The number of photons reached was on the same order of
magnitude as in Dwyer and Smith [2005] for a production altitude of 15 km, and more
than an order of magnitude more for production in 10 km altitude.
These calculations are average number of photons. As the lightning distribution
and the electric fields in the thunderstorms are varying one can expect the number
of photons to also follow a distribution. The fluence distribution was discussed in
Østgaard et al. [2012] (paper 1 of this thesis) using RHESSI, ADELE and the first
44
Source properties of TGFs
results from Fermi. After correcting for dead-time in RHESSI and the orbits of the
two satellite the fluence distribution was found to follow a power law with a power law
index of −2.3 ± 0.2 down to ∼5/600 of the detection threshold of RHESSI. Tierney
et al. [2013] did the same type of analysis for the new Fermi data reported on by Briggs
et al. [2013] and found a power law index of 2.20 ± 0.13.
These studies did not project the fluence back to the source as was done in Nisi
et al. [2014] (Paper 3 of this thesis). As the TGF travels through the atmosphere,
photons are attenuated in the air and TGFs from large distances will be detected with
a lower fluence due to the reduction in intensity with distance. The question is how
this may affect the fluence distribution. In Nisi et al. [2014], we used 10 years of
RHESSI data from the second catalog of TGFs. For about 300 TGFs (out of the 2500
total) we had a WWLLN match and was able to estimate the source location. As the
tropopause defines approximately the upper limit of the thunderclouds this was used as
an upper altitude for TGF production. To find the exact numbers we would need the
actual production altitude. By using the tropopause as an upper limit we found that
the fluence distribution changed to a slightly softer distribution when the altitude and
distance between the satellite and the source was taken into account.
Figure 5.11 is adapted from Nisi et al. [2014] (Paper 3 of this thesis) and shows
the fluence distribution for the dead time corrected measurements for a selection of the
RHESSI TGFs in red and the same sample corrected for the maximum source altitude
and distance from the satellite. To the two distributions a power law is fitted. This
shows that the projection down to the source region is important to estimate the fluence
correctly.
Figure 5.11: The fluence distribution of a selection of the second RHESSI catalog TGFs (red)
and the fluence distribution of the same selection when corrected for maximum production
altitude and distance from the satellite. This shows that the correction change the distribution
to a softer distribution, and that it is important to project the fluence back to the source. The
figure is adapted from Nisi et al. [2014].
5.7 Number of electrons
45
5.7 Number of electrons
From models Dwyer and Smith [2005] found that the number of high energy electrons
was of the same order as the number of high energy photons and concluded that the
number of electrons in a TGF is of the order of 1017 . The bremsstrahlung process was
modeled using the Born approximation together with a short wavelength correction.
As described in section 4.2, the influence of this assumption on the results are not
established. A model avoiding the Born approximation will be able to answer that
question.
The long spark experiments in Eindhoven described earlier has detectors that are
sensitive also to electrons, and only slightly sensitive to x-rays. This was done in order
to search for the high energy electrons that produce the x-rays in the spark. Together
with models this might make us able to investigate this further.
5.8 How the determination of source properties affects the theories
From the knowledge we have to this day, both the feedback theory and the thermal
runaway theory is both possible. However, the determination of the initial source properties support different theories.
Both the established theories involves electrical fields in the thunderstorm, so the altitude can not be used to differentiate between the two theories. However, establishing
the altitude might help determining the beaming of the photons as the angular distribution of the photons are be the main property left that changes the spectrum. In the
production region the shape of the electric field will partly determine the beaming, and
the direction of the electric field will determine the direction of the TGF. In a uniform
vertical field, the RREA will lead to a beam of electrons with a spread that drops to 1/2
at around 20 degrees off the vertical [Grefenstette et al., 2008; Hazelton et al., 2009].
If the field is diverging, the spread in the electrons will be larger. This means that if the
beaming of the electrons can be determined, this will give information on the shape of
the electric field.
What we observe in the TGF is light, so to determine the beaming of the electrons,
we will have to determine the beaming of the photons and also get the bremsstrahlung
process as accurately as possible. The bremsstrahlung process can be modeled, but to
establish if the >40 degree emission angles are a result of a sum of more narrow beams
with different directions or if this is the actual beaming more data is required.
Another parameter that will be important for establishing the full theory of production is the number of electrons. Here too, the determination of altitude would be helpful
as the attenuation of photons is highly dependent on the amount of air the TGF pass
through. Both the two theories have been shown to be able to produce 1017 electrons
within the duration of a TGF [Dwyer, 2007, 2008, 2012; Liu and Dwyer, 2013; Xu
et al., 2012]. However, if the number of electrons is much higher either because of the
source altitude being determined lower or the number of high energy photons produced
per electron seen to be smaller, one or both theories might fail.
A bremsstrahlung model avoiding the Born approximation might result in an improvement of the estimated number of photons/electrons. It would also improve the
predicted energy of the electrons producing the TGF. This might support one theory
46
Source properties of TGFs
more than the other and will also determine how important the RREA is to the process.
This is because the average energy for a RREA that has been going through several
avalanche lengths will be 7.3 MeV according to the empirical models [Dwyer et al.,
2012a].
The ratio of TGFs/lightning is also very important. The feedback theory will only
be creating a reasonable amount of photons if the available potential in the ambient
field of the thundercloud is of the order of about 100MV [Dwyer, 2007]. These high
potentials are only created in large thunderstorms and the TGF/lightning-ratio would
be expected to be small. The thermal runaway are able to create large numbers of
high energy photons from electric fields that are common in the tip of the lightning
streamers and leaders. Thus the ratio of TGFs/lightning can be expected to be much
larger if thermal runaway is what produces TGFs.
If we can establish the fluence distribution of TGFs, this might help answer this
question. If the power law index of the distribution is soft, we can expect that the observed number will increase much faster than for a harder distribution if the detection
threshold is reduced. And if the fluence has a roll off at low fluences this will give a
much larger number of TGFs per lightning than if there is a sharp cut off. If there is a
sharp cut off this will also imply that there is a lower limit of electrons/photons needed
to produce a TGF! If a cutoff is present just below 5/600 of RHESSI threshold, this
would imply a lowest number of 1014 photons per TGF, if the sensititvity is increased
to 1000 times the RHESSI sensititvity, the lowest number would be 1012 photons [Østgaard et al., 2012]. Lastly, if the x-rays from sparks are just low fluence TGFs, that
would suggest that the fluence do not have a sharp cut off.
Chapter 6
Introduction to the papers
Paper 1: The true fluence distribution of terrestrial gamma flashes at satellite altitude
To establish the fluence distribution for TGFs can help researchers to determin how
many TGFs occures globally and per lightning. However, the low fluence part of
the distribution is heavily affected by the number threshold of the instrument and the
high fluence region is affected by dead-time problems in the satellite. This paper used
RHESSI, Fermi and ADELE to investigate the fluence distribution. RHESSI was corrected for the known dead-time problems, and the satellites corrected for the differences
i n orbit to be comparable. The measurements from these two satellites gave a fluence
distribution with a power law of −2.3 ± 0.2. As the threshold of ADELE is much lower
than the two satellites, the detection of one TGF out of ∼ 1000 lightnings closer than
10 km from the aircraft and none out of ∼ 130 lightning closer than 4 km from the
satellite were used to adress the lower and of the spectrum. The conclution is that this
powe law continues down to at least 5/600 of the RHESSI threshold. Unless there is a
sharp cut of in the distribution below 5/600 of the RHESSI threshold, we can not rule
out that all lightning produce TGFs.
Paper 2: How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters
In this paper we investigate what we can expect to detect from TGFs using airborne instruments as balloons and aircrafts. The ADELE mission and forthcoming The Coupled
Observations from Balloon Related to Asim and Taranis (COBRAT) mission together
with other planned projects makes this highly interesting. We assessed this issue by using a Monte Carlo model of photon transport in air. In this model we start with a number of photons with specified initial energy and direction and propagate them through
the atmosphere. We then investigated how many photons went through a detector area
placed at different altitudes and horizontal distances from the initial position of the
starting point of the TGF. In order to find the limits of where the detectors mounted on
a balloon or aircraft can be expected to detect TGFs, we also used the model to get the
number of initial photons in a TGF. Both the number of initial photons and the limits
of detectability is of course highly dependent on the production altitude of the TGFs.
The fluence in 14 km altitude is 2-3 orders of magnitude larger for a TGF produced in
10 km than for a TGF produced in 20 km. Other important parameters are altitude dis-
48
Introduction to the papers
tribution, initial angular distribution of the photons and the amount of feedback. These
are especially important for observational altitudes lower than the production altitude
of the TGFs.
Paper 3: An altitude and distance correction to the initial fluence distribution of TGFs
In this paper we look at how the altitude and distance distribution affects the initial
fluence distribution. The study was made possible by the increased number of TGFs
in the second RHESSI catalog with connected geolocated lightning. Since TGFs from
deep in the atmosphere and/or from far distances will loose more photons between
the location of production and the satellite than the ones from high altitudes and close
regions, this might make the fluence distribution in the source look different then the
fluence distribution at the satellite. We use the tropopause altitude as an approximation
of the altitude distribution of the TGFs. With that we assume that the TGF altitude
distribution is following the tropopause distribution. We used the The National Centers
for Environmental Prediction (NCEP)/NCAR 40 years re-analysis 6 hour values to find
the tropopause pressure at the point with the highest tropopause altitude within the
satellite field of view. The distance and altitude correction makes the source fluence
distribution look slightly softer than the fluence distribution at the satellite showing
that these factors are important to take into account. When investigating the tropopause
altitudes at the time and location of TGFs, we also noticed that there is an annual
variation in the pressure for the tropics. This is explained in literature as being due to
a stronger Dobson-Brewer circulation in the north then in the south in the respective
winters. The importance of this in relation to TGF research is that the TGF/lightning
ratio can be expected to have a annual variability due to the easier escape of gamma
rays from the tropopause when the pressure is low.
Bibliography
Abarca, S. F., K. L. Corbosiero, and T. J. Galarneau (2010), An evaluation of the
Worldwide Lightning Location Network (WWLLN) using the National Lightning
Detection Network (NLDN) as ground truth, Journal of Geophysical Research,
115(D18206), doi:10.1029/2009JD013411. 2.3.1, 5.1.2
Babich, L. P., E. N. Donskoy, and R. A. Roussel-Dupré (2007), Study of relativistic electron avalanche enhancement in the atmosphere at low overvoltages due
to avalanche bremsstrahlung, Geomagnetism and Aeronomy, 47(4), 515–524, doi:
10.1134/S0016793207040135. 3.1
Babich, L. P., E. N. Donskoy, and I. M. Kutsyk (2008), Analysis of atmospheric
gamma-ray flashes detected in near space with allowance for the transport of photons in the atmosphere, Journal of Experimental and Theoretical Physics, 107(1),
49–60, doi:10.1134/S1063776108070042. 5.4
Boccippio, D. J., S. J. Goodman, and S. Heckman (2000), Regional Differences in
Tropical Lightning Distributions, Journal of Applied Meteorology, 39(12), 2231–
2248, doi:10.1175/1520-0450. 2.3.3
Briggs, M. S., G. J. Fishman, V. Connaughton, P. N. Bhat, W. S. Paciesas, R. D.
Preece, C. Wilson-Hodge, V. L. Chaplin, R. M. Kippen, A. von Kienlin, C. A.
Meegan, E. Bissaldi, J. R. Dwyer, D. M. Smith, R. H. Holzworth, J. E. Grove,
and A. Chekhtman (2010), First results on terrestrial gamma ray flashes from the
Fermi Gamma-ray Burst Monitor, Journal of Geophysical Research, 115(A07323),
doi:10.1029/2009JA015242. 2.1.4
Briggs, M. S., S. Xiong, V. Connaughton, D. Tierney, G. Fitzpatrick, S. Foley, J. E.
Grove, A. Chekhtman, M. Gibby, G. J. Fishman, S. McBreen, V. L. Chaplin,
S. Guiriec, E. Layden, P. N. Bhat, M. Hughes, J. Greiner, A. von Kienlin, R. M. Kippen, C. A. Meegan, W. S. Paciesas, R. D. Preece, C. Wilson-Hodge, R. H. Holzworth,
and M. L. Hutchins (2013), Terrestrial gamma-ray flashes in the Fermi era: Improved observations and analysis methods, Journal of Geophysical Research: Space
Physics, 118, 3805–3830, doi:10.1002/jgra.50205. 2.1.4, 5.1.1, 5.1.1, 5.1.2, 5.1.4,
5.1.4, 5.2.1, 5.2.1, 5.2.2, 5.6
Carlson, B. E., N. G. Lehtinen, and U. S. Inan (2007), Constraints on terrestrial
gamma ray flash production from satellite observation, Geophysical Research Letters, 34(L08809), doi:10.1029/2006GL029229. 5.4, 5.5
50
BIBLIOGRAPHY
Carlson, B. E., N. G. Lehtinen, and U. S. Inan (2009), Terrestrial gamma ray flash production by lightning current pulses, Journal of Geophysical Research, 114(A00E08),
doi:10.1029/2009JA014531. 5.2.2
Celestin, S., and V. P. Pasko (2011), Energy and fluxes of thermal runaway electrons
produced by exponential growth of streamers during the stepping of lightning leaders
and in transient luminous events, Journal of Geophysical Research, 116(A03315),
doi:10.1029/2010JA016260. 3.2.1, 3.3
Celestin, S., and V. P. Pasko (2012), Compton scattering effects on the duration of
terrestrial gamma-ray flashes, Geophysical Research Letters, 39(L02802), doi:10.
1029/2011GL050342. 5.1.4
Christian, H. J. (2003), Global frequency and distribution of lightning as observed from
space by the Optical Transient Detector, Journal of Geophysical Research, 108(D1),
doi:10.1029/2002JD002347. 2.3.3
Cohen, M. B., U. S. Inan, and E. W. Paschal (2010a), Sensitive Broadband ELF/VLF
Radio Reception With the AWESOME Instrument, IEEE Transactions on Geoscience and Remote Sensing, 48, doi:10.1109/TGRS.2009.2028334. 2.3.1
Cohen, M. B., U. S. Inan, R. K. Said, and T. Gjestland (2010b), Geolocation of terrestrial gamma-ray flash source lightning, Geophysical Research Letters, 37(L02801),
doi:10.1029/2009GL041753. 2.3.1
Collier, A. B., T. Gjesteland, and N. Østgaard (2011), Assessing the power law distribution of TGFs, Journal of Geophysical Research, 116(A10320), doi:10.1029/
2011JA016612. 2.3.1, 5.1.2, 5.1.5
Connaughton, V., M. S. Briggs, R. H. Holzworth, M. L. Hutchins, G. J. Fishman, C. A.
Wilson-Hodge, V. L. Chaplin, P. N. Bhat, J. Greiner, A. von Kienlin, R. M. Kippen,
C. A. Meegan, W. S. Paciesas, R. D. Preece, E. Cramer, J. R. Dwyer, and D. M. Smith
(2010), Associations between Fermi Gamma-ray Burst Monitor terrestrial gamma
ray flashes and sferics from the World Wide Lightning Location Network, Journal of
Geophysical Research, 115(A12307), doi:10.1029/2010JA015681. 2.3.1, 5.1.2
Connaughton, V., M. S. Briggs, S. Xiong, J. R. Dwyer, M. L. Hutchins, J. E. Grove,
A. Chekhtman, D. Tierney, G. Fitzpatrick, S. Foley, S. McBreen, P. N. Bhat, V. L.
Chaplin, E. Cramer, G. J. Fishman, R. H. Holzworth, M. Gibby, A. von Kienlin,
C. A. Meegan, W. S. Paciesas, R. D. Preece, and C. Wilson-Hodge (2013), Radio
signals from electron beams in terrestrial gamma ray flashes, Journal of Geophysical
Research: Space Physics, 118(5), 2313–2320, doi:10.1029/2012JA018288. 2.2.3,
5.1.5
Cooray, V. (2003), The Lightning Flash, iet power ed., 574 pp., The Institution of
Engineering and Technology, doi:10.1049/PBPO034E. 3.2.2
Cummer, S. A. (2005), Measurements and implications of the relationship between lightning and terrestrial gamma ray flashes, Geophysical Research Letters,
32(L08811), doi:10.1029/2005GL022778. 2.3.1, 5.2.1
BIBLIOGRAPHY
51
Cummer, S. A., G. Lu, M. S. Briggs, V. Connaughton, S. Xiong, G. J. Fishman, and
J. R. Dwyer (2011), The lightning-TGF relationship on microsecond timescales,
Geophysical Research Letters, 38(L14810), doi:10.1029/2011GL048099. 2.3.1,
5.1.5
Das, S. S., A. R. Jain, K. K. Kumar, and D. Narayana Rao (2008), Diurnal variability
of the tropical tropopause: Significance of VHF radar measurements, Radio Science,
43(RS6003), doi:10.1029/2008RS003824. 5.4
Dwyer, J. R. (2003), A fundamental limit on electric fields in air, Geophysical Research
Letters, 30(20), doi:10.1029/2003GL017781. 3.1, 3.4, 3.4, 3.4
Dwyer, J. R. (2004), A ground level gamma-ray burst observed in association with
rocket-triggered lightning, Geophysical Research Letters, 31(L05119), doi:10.1029/
2003GL018771. 2.2.2
Dwyer, J. R. (2005), The initiation of lightning by runaway air breakdown, Geophysical
Research Letters, 32(L20808), doi:10.1029/2005GL023975. 3.2.1
Dwyer, J. R. (2007), Relativistic breakdown in planetary atmospheres, Physics of Plasmas, 14(042901), doi:10.1063/1.2709652. 3.4, 3.4, 4, 4.2.3, 5.4, 5.8
Dwyer, J. R. (2008), Source mechanisms of terrestrial gamma-ray flashes, Journal of
Geophysical Research, 113(D10103), doi:10.1029/2007JD009248. 5.8
Dwyer, J. R. (2012), The relativistic feedback discharge model of terrestrial
gamma ray flashes, Journal of Geophysical Research, 117(A02308), doi:10.1029/
2011JA017160. 3.2.1, 5.8
Dwyer, J. R., and S. A. Cummer (2013), Radio emissions from terrestrial gamma-ray
flashes, Journal of Geophysical Research: Space Physics, 118(6), 3769–3790, doi:
10.1002/jgra.50188. 3.4
Dwyer, J. R., and D. M. Smith (2005), A comparison between Monte Carlo simulations
of runaway breakdown and terrestrial gamma-ray flash observations, Geophysical
Research Letters, 32(L22804), doi:10.1029/2005GL023848. 3.1, 5.4, 5.6, 5.7
Dwyer, J. R., M. A. Uman, H. K. Rassoul, M. Al-Dayeh, L. Caraway, J. Jerauld,
V. A. Rakov, D. M. Jordan, K. J. Rambo, V. Corbin, and B. Wright (2003), Energetic radiation produced during rocket-triggered lightning., Science (New York, N.Y.),
299(5607), 694–697, doi:10.1126/science.1078940. 2.4.1
Dwyer, J. R., H. K. Rassoul, M. Al-Dayeh, L. Caraway, B. Wright, A. Chrest, M. a.
Uman, V. a. Rakov, K. J. Rambo, D. M. Jordan, J. Jerauld, and C. Smyth (2004),
Measurements of x-ray emission from rocket-triggered lightning, Geophysical Research Letters, 31(L05118), doi:10.1029/2003GL018770. 2.4.1, 3.3
Dwyer, J. R., H. K. Rassoul, Z. H. Saleh, M. A. Uman, J. Jerauld, and J. A. Plumer
(2005), X-ray bursts produced by laboratory sparks in air, Geophysical Research
Letters, 32(L20809), doi:10.1029/2005GL024027. 2.4.2, 5.2.3
52
BIBLIOGRAPHY
Dwyer, J. R., Z. Saleh, H. K. Rassoul, D. Concha, M. Rahman, V. Cooray, J. Jerauld, M. A. Uman, and V. A. Rakov (2008), A study of X-ray emission from laboratory sparks in air at atmospheric pressure, Journal of Geophysical Research,
113(D23207), doi:10.1029/2008JD010315. 2.4.2, 5.2.3
Dwyer, J. R., D. M. Smith, and S. a. Cummer (2012a), High-Energy Atmospheric
Physics: Terrestrial Gamma-Ray Flashes and Related Phenomena, Space Science
Reviews, 173, 133–196, doi:10.1007/s11214-012-9894-0. 2.1.1, 3.1, 3.1, 3.4, 5.8
Dwyer, J. R., M. M. Schaal, E. Cramer, S. Arabshahi, N. Liu, H. K. Rassoul, J. D.
Hill, D. M. Jordan, and M. a. Uman (2012b), Observation of a gamma-ray flash at
ground level in association with a cloud-to-ground lightning return stroke, Journal of
Geophysical Research, 117(A10303), doi:10.1029/2012JA017810. 2.2.2
Elwert, G. (1939), Verschärfte Berechnung von Intensität und Polarisation im kontinuierlichen Röntgenspektrum1, Annalen der Physik, 426(2), 178–208, doi:10.1002/
andp.19394260206. 4.2.1, 4.2.3
Elwert, G., and E. Haug (1969), Calculation of Bremsstrahlung Cross Sections with
Sommerfeld-Maue Eigenfunctions, Physical Review, 183, 90–105, doi:10.1103/
PhysRev.183.90. 4.2.2
Feng, H., T. Li, M. Wu, M. Zha, and Q. Zhu (2002), Temporal and spectral properties
of gamma-ray flashes, Geophysical Research Letters, 29(3). 5.1.4
Fishman, G. J., P. N. Bhat, R. Mallozzi, J. M. Horack, T. Koshut, C. Kouveliotou,
N. Pendleton, C. A. Meegan, R. B. Wilson, W. S. Paciesas, S. J. Goodman, and H. J.
Christian (1994), Discovery of Intense Gamma-Ray Flashes of Atmospheric Origin,
Science, 264(5163), 1313–1316. 1, 2.1.1, 3.2, 5.1.1, 5.1.2, 5.3, 5.4
Fishman, G. J., M. S. Briggs, V. Connaughton, P. N. Bhat, W. S. Paciesas, A. von Kienlin, C. Wilson-Hodge, R. M. Kippen, R. Preece, C. A. Meegan, and J. Greiner (2011),
Temporal properties of the terrestrial gamma-ray flashes from the Gamma-Ray Burst
Monitor on the Fermi Observatory, Journal of Geophysical Research, 116(A07304),
doi:10.1029/2010JA016084. 2.1.4, 5.1.4
Foster, T., and J. Hallett (2002), The alignment of ice crystals in changing electric fields,
Atmospheric Research, 62(1-2), 149–169, doi:10.1016/S0169-8095(02)00008-X.
3.2.1
Fronsdal, C., and H. Uberall (1958), Polarization of Bremsstrahlung from Polarized
Electrons, Physical Review, 111(2), 580–586, doi:10.1016/0160-9327(74)90037-4.
4.2.2
Fueglistaler, S., A. E. Dessler, T. J. Dunkerton, I. Folkins, Q. Fu, and P. W. Mote
(2009), Tropical tropopause layer, Reviews of Geophysics, 47(RG1004), doi:10.
1029/2008RG000267. 5.2.1
Fuschino, F., M. Marisaldi, C. Labanti, G. Barbiellini, E. Del Monte, A. Bulgarelli,
M. Trifoglio, F. Gianotti, M. Galli, A. Argan, A. Trois, M. Tavani, E. Moretti, A. Giuliani, F. Longo, E. Costa, P. Caraveo, P. W. Cattaneo, A. Chen, F. D’Ammando,
BIBLIOGRAPHY
53
G. De Paris, G. Di Cocco, G. Di Persio, I. Donnarumma, Y. Evangelista, M. Feroci, A. Ferrari, M. Fiorini, I. Lapshov, F. Lazzarotto, P. Lipari, S. Mereghetti,
A. Morselli, L. Pacciani, A. Pellizzoni, F. Perotti, P. Picozza, G. Piano, M. Pilia,
M. Prest, G. Pucella, M. Rapisarda, A. Rappoldi, A. Rubini, S. Sabatini, P. Soffitta,
E. Striani, E. Vallazza, S. Vercellone, V. Vittorini, A. Zambra, D. Zanello, L. Antonelli, S. Colafrancesco, S. Cutini, P. Giommi, F. Lucarelli, C. Pittori, P. Santolamazza, F. Verrecchia, and L. Salotti (2011), High spatial resolution correlation of
AGILE TGFs and global lightning activity above the equatorial belt, Geophysical
Research Letters, 38(L14806), doi:10.1029/2011GL047817. 5.1.1, 5.2.2
Gjesteland, T., N. Østgaard, P. H. Connell, J. Stadsnes, and G. J. Fishman (2010), Effects of dead time losses on terrestrial gamma ray flash measurements with the Burst
and Transient Source Experiment, Journal of Geophysical Research, 115(A00E21),
doi:10.1029/2009JA014578. 5.4, 5.5
Gjesteland, T., N. Østgaard, A. B. Collier, B. E. Carlson, M. B. Cohen, and N. G.
Lehtinen (2011), Confining the Angular Distribution of Terrestrial Gamma-ray
Flash Emission., Journal of Geophysical Research, 116(A11313), doi:10.1029/
2011JA016716. 5.4, 5.5, 5.5
Gjesteland, T., N. Østgaard, A. B. Collier, B. E. Carlson, C. Eyles, and D. M. Smith
(2012), A new method reveals more TGFs in the RHESSI data, Geophysical Research Letters, 39(L05102), doi:10.1029/2012GL050899. 2.1.2, 5.1.1, 5.1.4, 5.2.2
Grefenstette, B. W., D. M. Smith, J. R. Dwyer, and G. J. Fishman (2008), Time evolution of terrestrial gamma ray flashes, Geophysical Research Letters, 35(L06802),
doi:10.1029/2007GL032922. 2.1.1, 2.1.1, 5.1.1, 5.1.4, 5.1.5, 5.4, 5.8
Grefenstette, B. W., D. M. Smith, B. J. Hazelton, and L. I. Lopez (2009), First RHESSI
terrestrial gamma ray flash catalog, Journal of Geophysical Research, 114(A02314),
doi:10.1029/2008JA013721. 2.1.2
Griffiths, R. F., and J. Latham (1972), The Emission of Corona from falling drops,
Journal of the Meteorological Society of Japan, 50(5), 416–422. 3.2.1
Gurevich, A. V., G. M. Milikh, and R. A. Roussel-Dupré (1992), Runaway electron
mechanism of air breakdown and preconditioning during a thunderstorm, Physics
Letters A, 165(5-6), 463–468, doi:10.1016/0375-9601(92)90348-P. 3.2.1
Gurevich, A. V., G. M. Milikh, and J. A. Valdivia (1997), Model of X-ray emission and
fast preconditioning during a thunderstorm, Physics Letters A, 231, 402–408. 3.2.1
Gurevich, A. V., K. P. Zybin, and R. A. Roussel-Dupré (1999), Lightning initiation by
simultaneous effect of runaway breakdown and cosmic ray showers, Physics Letters
A, 254, 79–87. 3.2.1
Hansen, R. S., N. Østgaard, T. Gjesteland, and B. Carlson (2013), How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes
depends on initial parameters, Journal of Geophysical Research: Space Physics, 118,
2333–2339, doi:10.1002/jgra.50143. 2.2.4, 5.2.2, 5.4, 5.6
54
BIBLIOGRAPHY
Haug, E. (2008), Bremsstrahlung cross-section with screening and Coulomb corrections at high energies, Radiation Physics and Chemistry, 77(3), 207–214, doi:
10.1016/j.radphyschem.2007.10.003. 4.2.2, 4.2.2
Haug, E., and W. Nakel (2004), The Elementary Process of Bremsstrahlung, vol. 73,
chap. 3, World Scientific Lecture Notes in Physics. 4.2, 4.2.1, 4.2.1
Hazelton, B. J., B. W. Grefenstette, D. M. Smith, J. R. Dwyer, X.-M. Shao, S. A.
Cummer, T. Chronis, E. H. Lay, and R. H. Holzworth (2009), Spectral dependence
of terrestrial gamma-ray flashes on source distance, Geophysical Research Letters,
36(L01108), doi:10.1029/2008GL035906. 5.1.2, 5.4, 5.5, 5.8
Knoll, G. E. (2000), Radiation Detection and Measurement, 3rd edition ed., 802 pp.,
John Wiley & Sons, Inc. 2.1.1
Koch, H. W., and J. W. Motz (1959), Bremsstrahlung Cross-Section Formulas and
Related Data, Reviews of modern physics, 31(4). 4.2.1
Kochkin, P. O., C. V. Nguyen, A. P. J. van Deursen, and U. Ebert (2012), Experimental
study of hard x-rays emitted from metre-scale positive discharges in air, Journal
of Physics D: Applied Physics, 45(425202), doi:10.1088/0022-3727/45/42/425202.
2.4.2, 2.4.2, 3.3, 5.2.3
Köhn, C., and U. Ebert (2014), Angular distribution of Bremsstrahlung photons and of
positrons for calculations of terrestrial gamma-ray flashes and positron beams, Atmospheric Research, 135-136, 432–465, doi:10.1016/j.atmosres.2013.03.012. 4.2.3
Kulak, A., J. Mlynarczyk, M. Ostrowski, J. Kubisz, and A. Michalec (2012), Analysis
of ELF electromagnetic field pulses recorded by the Hylaty station coinciding with
terrestrial gamma-ray flashes, Journal of Geophysical Research, 117(D18203), doi:
10.1029/2012JD018205. 2.3.1
Lehtinen, N. G., M. Walt, U. S. Inan, T. F. Bell, and V. P. Pasko (1996), y-ray emission produced by a relativistic beam of runaway electrons accelerated by quasielectrostatic thundercloud fields, Geophysical Research Letters, 23(19), 2645–2648.
4.2.3
Liu, C., and E. J. Zipser (2005), Global distribution of convection penetrating the
tropical tropopause, Journal of Geophysical Research, 110(D23), D23,104, doi:
10.1029/2005JD006063. 5.4
Liu, N., and J. R. Dwyer (2013), Modeling terrestrial gamma ray flashes produced by
relativistic feedback discharges, Journal of Geophysical Research: Space Physics,
118(5), 2359–2376, doi:10.1002/jgra.50232. 3.2.1, 5.8
Lu, G., R. J. Blakeslee, J. Li, D. M. Smith, X.-M. Shao, E. W. McCaul, D. E. Buechler,
H. J. Christian, J. M. Hall, and S. A. Cummer (2010), Lightning mapping observation
of a terrestrial gamma-ray flash, Geophysical Research Letters, 37(L11806), doi:
10.1029/2010GL043494. 2.3.2, 5.1.5, 5.2.1, 5.4
BIBLIOGRAPHY
55
Mallios, S. A., S. Celestin, and V. P. Pasko (2013), Production of very high potential
differences by intracloud lightning discharges in connection with terrestrial gamma
ray flashes, Journal of Geophysical Research: Space Physics, 118, 912–918, doi:
10.1002/jgra.50109. 3.3
Marisaldi, M., A. Argan, A. Trois, A. Giuliani, M. Tavani, C. Labanti, F. Fuschino,
A. Bulgarelli, F. Longo, G. Barbiellini, E. Del Monte, E. Moretti, M. Trifoglio,
E. Costa, P. Caraveo, P. Cattaneo, A. Chen, F. D’Ammando, G. De Paris, G. Di
Cocco, G. Di Persio, I. Donnarumma, Y. Evangelista, M. Feroci, A. Ferrari,
M. Fiorini, T. Froysland, M. Galli, F. Gianotti, I. Lapshov, F. Lazzarotto, P. Lipari, S. Mereghetti, A. Morselli, L. Pacciani, A. Pellizzoni, F. Perotti, P. Picozza,
G. Piano, M. Pilia, M. Prest, G. Pucella, M. Rapisarda, A. Rappoldi, A. Rubini,
S. Sabatini, P. Soffitta, E. Striani, E. Vallazza, S. Vercellone, V. Vittorini, A. Zambra, D. Zanello, L. Antonelli, S. Colafrancesco, S. Cutini, P. Giommi, F. Lucarelli,
C. Pittori, P. Santolamazza, F. Verrecchia, and L. Salotti (2010a), Gamma-Ray Localization of Terrestrial Gamma-Ray Flashes, Physical Review Letters, 105(128501),
doi:10.1103/PhysRevLett.105.128501. 2.1.3
Marisaldi, M., F. Fuschino, C. Labanti, M. Galli, F. Longo, E. Del Monte, G. Barbiellini, M. Tavani, A. Giuliani, E. Moretti, S. Vercellone, E. Costa, S. Cutini, I. Donnarumma, Y. Evangelista, M. Feroci, I. Lapshov, F. Lazzarotto, P. Lipari, S. Mereghetti, L. Pacciani, M. Rapisarda, P. Soffitta, M. Trifoglio, A. Argan, F. Boffelli, A. Bulgarelli, P. Caraveo, P. W. Cattaneo, A. Chen, V. Cocco,
F. D’Ammando, G. De Paris, G. Di Cocco, G. Di Persio, A. Ferrari, M. Fiorini,
T. Froysland, F. Gianotti, A. Morselli, A. Pellizzoni, F. Perotti, P. Picozza, G. Piano, M. Pilia, M. Prest, G. Pucella, A. Rappoldi, A. Rubini, S. Sabatini, E. Striani,
A. Trois, E. Vallazza, V. Vittorini, A. Zambra, D. Zanello, L. A. Antonelli, S. Colafrancesco, D. Gasparrini, P. Giommi, C. Pittori, B. Preger, P. Santolamazza, F. Verrecchia, and L. Salotti (2010b), Detection of terrestrial gamma ray flashes up to 40
MeV by the AGILE satellite, Journal of Geophysical Research, 115(A00E13), doi:
10.1029/2009JA014502. 5.3
Marisaldi, M., F. Fuschino, M. Tavani, S. Dietrich, C. Price, M. Galli, C. Pittori, F. Verrecchia, S. Mereghetti, P. W. Cattaneo, S. Colafrancesco, A. Argan, C. Labanti,
F. Longo, E. Del Monte, G. Barbiellini, A. Giuliani, A. Bulgarelli, R. Campana,
A. Chen, F. Gianotti, P. Giommi, F. Lazzarotto, A. Morselli, M. Rapisarda, A. Rappoldi, M. Trifoglio, A. Trois, and S. Vercellone (2014), Properties of Terrestrial
Gamma-Ray Flashes detected by AGILE MCAL below 30 MeV, Journal of Geophysical Research: Space Physics, 119, 1337–1355, doi:10.1002/2013JA019301.
2.1.3
Marshall, T. C., and M. Stolzenburg (2001), Voltages inside and just above thunderstorms, Journal of Geophysical Research, 106(D5), 4757–4768, doi:10.1029/
2000JD900640. 3.2
Meegan, C., G. Lichti, P. N. Bhat, E. Bissaldi, M. S. Briggs, V. Connaughton, R. Diehl,
G. Fishman, J. Greiner, A. S. Hoover, A. J. van der Horst, A. von Kienlin, R. M.
Kippen, C. Kouveliotou, S. McBreen, W. S. Paciesas, R. Preece, H. Steinle, M. S.
Wallace, R. B. Wilson, and C. Wilson-Hodge (2009), The Fermi Gamma-Ray Burst
56
BIBLIOGRAPHY
Monitor, The Astrophysical Journal, 702, 791–804, doi:10.1088/0004-637X/702/1/
791. 2.1.4
Moore, C. B., K. B. Eack, G. D. Aulich, and W. Rison (2001), Energetic radiation associated with lightning stepped leaders, Geophysical Research Letters, 28(11), 2141–
2144. 2.4.1
Moss, G. D., V. P. Pasko, N. Liu, and G. Veronis (2006), Monte Carlo model for analysis of thermal runaway electrons in streamer tips in transient luminous events and
streamer zones of lightning leaders, Journal of Geophysical Research, 111(A02307),
doi:10.1029/2005JA011350. 3.1, 3.2.2, 3.3
Nakel, W. (1994), The elementary process of bremsstrahlung, Physics Reports, 243(6),
317–353, doi:10.1016/0370-1573(94)00068-9. 4.2.1
Nemiroff, R. J., J. T. Bonnell, and J. P. Norris (1997), Temporal and spectral characteristics of terrestrial gamma flashes, Journal of Geophysical Research, 102(A5),
9659–9665. 2.1.1, 5.1.4, 5.1.4
Nisi, R. S., N. Østgaard, T. Gjesteland, and A. Collier (2014), An altitude and distance
correction to the initial fluence distribution of TGFs, Submitted. 5.1.1, 5.1.2, 5.2.1,
5.6
Olsen, H., L. C. Maximon, and H. Wergeland (1957), Theory of High-Energy
Bremsstrahlung and Pair Production in a Screened Field, Physical Review, 106(1),
27–46. 4.2.2
Østgaard, N., T. Gjesteland, J. Stadsnes, P. H. Connell, and B. Carlson (2008), Production altitude and time delays of the terrestrial gamma flashes: Revisiting the Burst and
Transient Source Experiment spectra, Journal of Geophysical Research, 113(A2), 1–
14, doi:10.1029/2007JA012618. 2.1.1, 4.1, 5.1.4, 5.4, 5.5
Østgaard, N., T. Gjesteland, R. S. Hansen, A. B. Collier, and B. Carlson (2012), The
true fluence distribution of terrestrial gamma flashes at satellite altitude, Journal
of Geophysical Research, 117(A03327), doi:10.1029/2011JA017365. 2.1.2, 5.2.1,
5.2.2, 5.2.2, 5.6, 5.8
Østgaard, N., T. Gjesteland, B. E. Carlson, A. B. Collier, S. a. Cummer, G. Lu, and
H. J. Christian (2013), Simultaneous observations of optical lightning and terrestrial
gamma ray flash from space, Geophysical Research Letters, 40, 2423–2426, doi:
10.1002/grl.50466. 2.2.3, 5.1.5, 5.2.1
Petersen, D., M. Bailey, J. Hallett, and W. H. Beasley (2006), Laboratory investigation
of positive streamer discharges from simulated ice hydrometeors, Quarterly Journal
of the Royal Meteorological Society, 132(615), 263–273, doi:10.1256/qj.05.32. 3.2.1
Reid, G. C., and K. S. Gage (1996), The tropical tropopause over the western Pacific:
Wave driving, convection, and the annual cycle, Journal of Geophysical Research,
101(96), 21,233–21,241. 5.2.1
BIBLIOGRAPHY
57
Roche, G., C. Ducos, and J. Proriol (1972), Bremsstrahlung Cross-Section Formula
Including a High-Order Coulumb Correction, Physical Review A, 5(6), 2403–2408.
4.2.2, 4.2.2
Roussel-Dupré, R., and A. V. Gurevich (1996), On runaway breakdown and upward
propagating discharges, Journal of Geophysical Research, 101(A2), 2297–2311, doi:
10.1029/95JA03278. 3.1
Roussel-Dupré, R. A., A. V. Gurevich, T. Tunnell, and G. M. Milikh (1994), Kinetic
theory of runaway air breakdown, Physical review Ei, 49(3). 3.1
Saunders, C. (2008), Charge Separation Mechanisms in Clouds, Space Science Reviews, 137, 335–353, doi:10.1007/s11214-008-9345-0. 3.2
Seidel, D. J., and W. J. Randel (2006), Variability and trends in the global tropopause
estimated from radiosonde data, Journal of Geophysical Research, 111(D21101),
doi:10.1029/2006JD007363. 5.4
Seltzer, S., and M. Berger (1985), Bremsstrahlung spectra from electron interactions
with screened atomic nuclei and orbital electrons, Nuclear Instruments and Methods
in Physics Research Section B: Beam Interactions with Materials and Atoms, 12,
95–134, doi:10.1016/0168-583X(85)90707-4. 4.2.3
Seltzer, S., and M. Berger (1986), Bremsstrahlung energy spectra from electrons with
kinetic energy 1 keV?10 GeV incident on screened nuclei and orbital electrons of
neutral atoms with = 1?100, Atomic Data and Nuclear Data Tables, 35, 345–418,
doi:10.1016/0092-640X(86)90014-8. 4.2.3
Shao, X.-M., T. Hamlin, and D. M. Smith (2010), A closer examination of terrestrial gamma-ray flash-related lightning processes, Journal of Geophysical Research,
115(A00E30), doi:10.1029/2009JA014835. 2.3.2, 5.2.1, 5.4
Smith, D. M. (2002), The rhessi spectrometer, Solar Physics, 210, 33–60. 2.1.2
Smith, D. M., L. I. Lopez, R. P. Lin, and C. P. Barrington-Leigh (2005), Terrestrial
gamma-ray flashes observed up to 20 MeV., Science, 307, 1085–1088, doi:10.1126/
science.1107466. 5.1.1, 5.3, 5.4
Smith, D. M., B. J. Hazelton, B. W. Grefenstette, J. R. Dwyer, R. H. Holzworth,
and E. H. Lay (2010), Terrestrial gamma ray flashes correlated to storm phase and
tropopause height, Journal of Geophysical Research, 115(A00E49), doi:10.1029/
2009JA014853. 5.2.2
Smith, D. M., J. R. Dwyer, B. J. Hazelton, B. W. Grefenstette, G. F. M. MartinezMcKinney, Z. Y. Zhang, A. W. Lowell, N. A. Kelley, M. E. Splitt, S. M. Lazarus,
W. Ulrich, M. Schaal, Z. H. Saleh, E. Cramer, H. K. Rassoul, S. A. Cummer, G. Lu,
and R. J. Blakeslee (2011a), The rarity of terrestrial gamma-ray flashes, Geophysical
Research Letters, 38(L08807), doi:10.1029/2011GL046875. 2.2.1, 5.2.2, 5.4
58
BIBLIOGRAPHY
Smith, D. M., S. M. Lazarus, W. Ulrich, M. Schaal, Z. Saleh, E. Cramer, H. K. Rassoul, S. A. Cummer, G. Lu, X.-M. Shao, C. Ho, J. R. Dwyer, T. Hamlin, R. J.
Blakeslee, S. J. Heckman, B. J. Hazelton, B. W. Grefenstette, G. F. M. MartinezMcKinney, Z. Y. Zhang, A. W. Lowell, N. A. Kelley, and M. E. Splitt (2011b), A
terrestrial gamma-ray flash observed from an aircraft, Journal of Geophysical Research, 116(D20124), doi:10.1029/2011JD016252. 2.2.1, 5.2.2, 5.2.2
Splitt, M. E., S. M. Lazarus, D. Barnes, J. R. Dwyer, H. K. Rassoul, D. M. Smith,
B. Hazelton, and B. Grefenstette (2010), Thunderstorm characteristics associated
with RHESSI identified terrestrial gamma ray flashes, Journal of Geophysical Research, 115(A00E38), doi:10.1029/2009JA014622. 5.1.1, 5.1.3, 5.2.1
Stanley, M. A., X.-M. Shao, D. M. Smith, L. I. Lopez, M. B. Pongratz, J. D. Harlin,
M. Stock, and A. Regan (2006), A link between terrestrial gamma-ray flashes and
intracloud lightning discharges, Geophysical Research Letters, 33(L06803), doi:10.
1029/2005GL025537. 2.3.2, 5.2.1, 5.4
Stolzenburg, M., and T. C. Marshall (2008), Charge Structure and Dynamics in Thunderstorms, Space Science Reviews, 137, 355–372, doi:10.1007/s11214-008-9338-z.
3.2, 3.2
Stolzenburg, M., W. D. Rust, and T. C. Marshall (1998), Electrical structure in thunderstorm convective regions 3. Synthesis, Journal of Geophysical Research, 103(D12),
14,097–14,108, doi:10.1029/97JD03545. 3.2
Tavani, M., M. Marisaldi, C. Labanti, F. Fuschino, A. Argan, a. Trois, P. Giommi,
S. Colafrancesco, C. Pittori, F. Palma, M. Trifoglio, F. Gianotti, A. Bulgarelli, V. Vittorini, F. Verrecchia, L. Salotti, G. Barbiellini, P. Caraveo, P. Cattaneo, A. Chen,
T. Contessi, E. Costa, F. D’Ammando, E. Del Monte, G. De Paris, G. Di Cocco, G. Di
Persio, I. Donnarumma, Y. Evangelista, M. Feroci, A. Ferrari, M. Galli, A. Giuliani,
M. Giusti, I. Lapshov, F. Lazzarotto, P. Lipari, F. Longo, S. Mereghetti, E. Morelli,
E. Moretti, A. Morselli, L. Pacciani, A. Pellizzoni, F. Perotti, G. Piano, P. Picozza,
M. Pilia, G. Pucella, M. Prest, M. Rapisarda, A. Rappoldi, E. Rossi, A. Rubini,
S. Sabatini, E. Scalise, P. Soffitta, E. Striani, E. Vallazza, S. Vercellone, A. Zambra,
and D. Zanello (2011), Terrestrial Gamma-Ray Flashes as Powerful Particle Accelerators, Physical Review Letters, 106(018501), doi:10.1103/PhysRevLett.106.018501.
2.1.3
Tierney, D., M. S. Briggs, G. Fitzpatrick, V. L. Chaplin, S. Foley, S. McBreen, V. Connaughton, S. Xiong, D. Byrne, M. Carr, P. N. Bhat, G. J. Fishman, J. Greiner, R. M.
Kippen, C. A. Meegan, W. S. Paciesas, R. D. Preece, A. von Kienlin, and C. WilsonHodge (2013), Fluence distribution of terrestrial gamma ray flashes observed by the
Fermi Gamma-ray Burst Monitor, Journal of Geophysical Research: Space Physics,
118, 6644–6650, doi:10.1002/jgra.50580. 5.3, 5.6
Williams, E. R. (2006), Problems in lightning physics—the role of polarity asymmetry,
Plasma Sources Science and Technology, 15(2), S91–S108, doi:10.1088/0963-0252/
15/2/S12. 3.2
BIBLIOGRAPHY
59
Wilson, C. T. R. (1924), The electric field of a thundercloud and some of its effects, Proceedings of the Physical Society of London, 37(1), 32D–37D, doi:10.1088/
1478-7814/37/1/314. 3.1
Xu, W., S. Celestin, and V. P. Pasko (2012), Source altitudes of terrestrial gamma-ray
flashes produced by lightning leaders, Geophysical Research Letters, 39(8), L08,801,
doi:10.1029/2012GL051351. 5.8
60
BIBLIOGRAPHY
Acronyms
ADELE
The Airborne Detector for Energetic Lightning Emissions.
AGILE
The Astrorivelatore Gamma a Immagini Leggero.
AWESOME The Atmospheric Weather Electromagnetic System for Observation,
Modeling, and Education.
BATSE
The Burst and Transient Source Experiment.
BGO
Bismuth Germanate.
CG
Cloud to Ground.
CGRO
The Compton Gamma-Ray Observatory.
COBRAT
The Coupled Observations from Balloon Related to Asim and
Taranis.
DJF
December, January and February.
ELF
Extreme Low Frequency.
Fermi
The Fermi Gamma-ray Space Telescope.
GBM
The Gamma-ray Burst Monitor.
GRB
Gamma-Ray Burst.
GV
The Gulfstream V jet.
HF
High Frequency.
IC
Intra Cloud.
JJA
June, July and August.
LASA
The Los Alamos Spheric Array.
LIS
The Lightning Imaging Sensor.
LMA
The Lightning Mapping Array.
MC
Monte Carlo.
62
Acronyms
MCAL
The Mini-Calorimeter.
NaI
Sodium Iodide.
NCAR
The National Center for Atmospheric Research.
NCEP
The National Centers for Environmental Prediction.
NLDN
The National Lightning Detection Network.
OTD
The Optical Transient Detector.
RHESSI
The Reuven Ramaty High Energy Solar Spectroscopic Imager.
RREA
Relativistic Runaway Electron Avalanche.
TRMM
The Tropical Rainfall Measuring Mission.
VHF
Very High Frequency.
VLF
Very Low Frequency.
WWLLN
The World Wide Lightning Location Network.
Nomenclature
α
The fine structure constant, α = 1/137.
β1
The energy of the incoming electron in the bremsstrahlung process
in units of the light velocity.
β2
The energy of the outgoing electron in the bremsstrahlung process
in units of the light velocity.
E
Electric field strength.
ε
The energy of an electron.
εth
The minimum energy for an electron to be a seed electron for an
electric field of strength E.
ε1
The energy of the incomming electron in Bremsstrahlung
calculations.
ε2
The energy of the outgoing electron in Bremsstrahlung calculations.
Eb
The smallest electrical field that can give runaway electrons, Eb ≈
200 kV/m.
Ec
The critical electric field to accelerate low energy electrons to relativistic energies, Ec ≈32 MV/m.
Ek
The conventional breakdown electric field, Ek ≈3.2 MV/m.
Est−
The electric field required for a negative streamer to form,
Est− ≈1200 kV/m.
Est+
The electric field required for a positive streamer to form, Est+ ≈440
kV/m.
Et h
The threshold electric field for the Relativistic Runaway Electron
Avalanche. Eb ≈ 2.8 × 105 V/m.
F0
The number of initial seed electrons in a Relativistic Runaway Electron Avalanche.
64
Nomenclature
Fd
The average energy loss rate for the electrons in the direction of the
avalanche in a Relativistic Runaway Electron Avalanche, Fd ≈0.275
MeV/m.
FE
The Elwert factor, a correction factor to get a finite cross section at the short wave limit in the Born approximation, used in
bremsstrahlung calculations..
Ff b
The number of electrons produced in the feedback process.
fre
Runaway electrons per unit energy after a Relativistic Runaway
Electron Avalanche.
FRREA The number of electrons created in a Relativistic Runaway Electron
Avalanche.
γ
The feedback factor, defined as the number of new avalanches created by each Relativistic Runaway Electron Avalanche.
k
The energy of the photon produced in the Bremsstrahlung process.
L
The total length of the avalanche region in a Relativistic Runaway
Electron Avalanche.
λ
The avalanche length of a Relativistic Runaway Electron Avalanche
defined as the length the avalanche needs for the number of photons
to increase by e.
|M|
The matrix element for the electron transition 1→2 of the Hamiltonian of the electron in the interaction of a radiation field, used in the
bremsstrahlung calculations.
Ω
Denotes solid angle in Bremsstrahlung calculations.
p1
The momentum of the incoming electron in Bremsstrahlung
calculations.
p2
The momentum of the outgoing electron in Bremsstrahlung
calculations.
R
The radial distance from the source of a TGF to the point of
measurement.
σ
The standard deviation of a distribution.
τ
The time of one feedback cycle.
t90
The length of the interval in which 90% of the counts are accumulated, with 5% of the counts occurring before and 5% after this
interval.
Nomenclature
z
The distance from the start of the avalanche in Relativistic Runaway
Electron Avalanche.
65
66
Nomenclature
Scientific results
68
Scientific results
Paper 1
6.1 The true fluence distribution of terrestrial gamma flashes at satellite altitude
Østgaard, N., Gjesteland, T., Hansen, R. S., Collier, A. B., and Carlson, B.
Journal of Geophysical Research Space Physics, 117(A03327), doi:10.1029/2011JA017365,
2012
70
Scientific results
6.1 The true fluence distribution of terrestrial gamma flashes at satellite altitude
71
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, A03327, doi:10.1029/2011JA017365, 2012
The true fluence distribution of terrestrial gamma flashes
at satellite altitude
N. Østgaard,1 T. Gjesteland,1 R. S. Hansen,1 A. B. Collier,2,3 and B. Carlson1
Received 11 November 2011; revised 20 January 2012; accepted 1 February 2012; published 24 March 2012.
[1] In this paper we use the fluence distributions observed by two different instruments,
RHESSI and Fermi GBM, corrected for the effects of their different orbits, combined
with their different daily TGF detection rates and their relative sensitivities to make an
estimate of the true fluence distribution of TGFs as measured at satellite altitudes.
The estimate is then used to calculate the dead-time loss for an average TGF measured
by RHESSI. An independent estimate of RHESSI dead-time loss and true fluence
distribution is obtained from a Monte Carlo (MC) simulation in order to evaluate the
consistency of our results. The two methods give RHESSI dead-time losses of 24–26% for
average fluence of 33–35 counts. Assuming a sharp cut-off the true TGF fluence
distribution is found to follow a power law with l = 2.3 0.2 down to 5/600 of the
detection threshold of RHESSI. This corresponds to a lowest number of electrons produced
in a TGF of 1014 and a global production rate within 38 latitude of 50000 TGFs/day
or about 35 TGFs every minute, which is 2% of all IC lightning. If a more realistic
distribution with a roll-off below 1/3 (or higher) of the RHESSI lower detection
threshold with a true distribution with l ≤ 1.7 that corresponds to a source distribution with
l ≤ 1.3 is considered, we can not rule out that all discharges produce TGFs. In that case
the lowest number of total electrons produced in a TGF is 1012.
Citation: Østgaard, N., T. Gjesteland, R. S. Hansen, A. B. Collier, and B. Carlson (2012), The true fluence distribution of
terrestrial gamma flashes at satellite altitude, J. Geophys. Res., 117, A03327, doi:10.1029/2011JA017365.
1. Introduction
[2] With the discovery of terrestrial gamma flashes
(TGFs) above thunderstorms [Fishman et al., 1994] by the
Burst and Transient Source Experiment (BATSE) a new
mechanism of the coupling between the lower atmosphere
and space was found. The phenomenon involves both
gamma photons, relativistic electrons and positrons.
Charged particles are accelerated in extremely strong
electric fields (>300 kV/m sea level equivalent) associated
with lightning discharges and initiate a relativistic runaway process [Gurevich et al., 1992]. Through interaction
with the neutral atmosphere bremsstrahlung is produced,
resulting in the escape of electrons [Dwyer et al., 2008],
positrons [Briggs et al., 2011] and gamma photons into
space. There are still many open questions related to TGFs,
and one of them will be addressed in this paper: How
common are TGFs? Or more specifically: What is the true
fluence distribution of TGFs as measured from satellite
altitude?
[3] From the first observations it was believed that the
TGFs are produced above 40 km and that they were related
1
Department of Physics and Technology, University of Bergen, Bergen,
Norway.
2
SANSA Space Science, Hermanus, South Africa.
3
University of KwaZulu-Natal, Durban, South Africa.
Copyright 2012 by the American Geophysical Union.
0148-0227/12/2011JA017365
to transient luminous events [Fishman et al., 1994; Nemiroff
et al., 1997], a reasonable suggestion given the relatively few
observations of about 10 TGF/year by BATSE (78 TGFs in
9 years according to http://www.batse.msfc.nasa.gov/batse/
misc/triggers.html). However, results from Reuvan Ramaty
High Energy Solar Spectroscopic Imager (RHESSI) ten years
later indicated that their production altitude is most likely
around 15–21 km [Dwyer and Smith, 2005]. While BATSE
had an on-board trigger algorithm with a 64 ms search window, the data from RHESSI were downloaded and a more
sophisticated, but still rather conservative, search algorithm
with a search window of 1 ms was applied. For more details
about the search algorithm we refer to Grefenstette et al.
[2009]. Having a trigger window significantly longer than
the typical duration of a TGF(<1 ms), like BATSE had, only
events with high count rates that exceed the statistical fluctuations of background counts will be classified as TGFs.
However, RHESSI had a search window comparable to the
duration of a TGF and could identify much weaker TGFs.
Thus, RHESSI was able to report more than 100 TGFs/year
(975 TGFs in 8.5 years according to http://scipp.ucsc.edu/
dsmith/tgflib_public/). Reanalyses of the BATSE data have
also confirmed a production altitude of TGFs below 20 km
[Carlson et al., 2007; Østgaard et al., 2008; Gjesteland et al.,
2010]. Consistent with this production altitude and general
lightning physics, Williams [2006] speculated that TGFs are
related to positive intracloud lightning, a suggestion that has
been supported by a few studies comparing TGFs with
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Scientific results
ØSTGAARD ET AL.: TGF FLUENCE DISTRIBUTION FROM SPACE
A03327
ADELE’s sensitivity and the non-detection of TGFs by
this aircraft.
2. The Measured TGF Fluence Distributions and
Average Duration
Figure 1. The fluence distributions of TGFs measured by
RHESSI (grey histogram) and Fermi (black histogram).
Power functions are fitted to both distributions. The average
values for Fermi are for TGF pulses, defined as counts in the
central 50% of duration.
electromagnetic characteristics of lightning [Cummer et al.,
2005; Shao et al., 2010; Cummer et al., 2011]. As intracloud lightning accounts for about 75% of all the lightning
[Boccippio et al., 2001] and most of these are positive
intracloud lightning bringing negative charges upward, this
may imply that TGFs are a rather common phenomenon.
X-ray bursts have been observed from negative leader steps
in cloud-to-ground (CG–) lightning [Dwyer et al., 2005] and
from dart leaders in rocket triggered lightning [Dwyer et al.,
2004] before the return strokes of the CG– lightning. Discharge experiments in the laboratory [Nguyen et al., 2008]
have also shown that bursts of X-rays are observed slightly
before (1 ms) the discharge return stroke. All these studies
give some hints that TGFs might be more common than
observations from space have indicated so far. On the other
hand, Smith et al. [2011] suggested that the non-detection of
TGFs by the Airborne Detector for Energetic Lightning
Emissions (ADELE) may indicate the opposite, that there
are very few TGFs with intensities two-three orders of
magnitude weaker than those observed by RHESSI.
[4] Measurements from space have been hampered by the
loss of counts due to dead-time in the electronics, limited
instrument sensitivity and limitations due to the on-board
trigger window. In this paper we will use the fluence distributions observed by two different instruments, RHESSI
and Fermi GBM, corrected for the effects of their different
orbits, combined with their different daily TGF detection
rates and their relative sensitivities to make an estimate of
the true fluence distribution of TGFs at satellite altitudes.
This estimate is then used to calculate the dead-time loss
for an average TGF fluence measured by RHESSI. Independent estimates of RHESSI dead-time loss and true fluence distribution are obtained from a Monte Carlo (MC)
simulation in order to evaluate the consistency of our
results. Finally, we discuss our results in the context of
[5] The fluence distribution of the 591 TGFs measured by
RHESSI (March 4, 2002–December 31, 2005) and the first
53 TGFs measured by Fermi (Aug 7, 2008–March 10, 2010)
are shown in Figure 1. The RHESSI TGFs were downloaded
from http://scipp.ucsc.edu/dsmith/tgflib_public/ and are
the same as used in the quantitatively analysis by
Grefenstette et al. [2009] obtained before the degradation of
the instrument’s sensitivity when the effective detector area
was still 256 cm2. The Fermi TGFs are taken from Fishman
et al. [2011, Table 2]. The three double peaks in that table
are treated as separate TGFs giving a total of 53 TGF pulses.
All these TGFs were detected when an on-board 16 ms
trigger window was used. A power function with the form
dN
¼ A0 n
dn
l
ð1Þ
(dN is the number of TGFs with fluence within dn and A0 is a
scaling factor) has been fitted to each of the distribution,
giving l of 3.5 and 1.4, for RHESSI and Fermi, respectively.
The fit is based on 14 (4) bins from the peak using bin size of
2 (50) counts for the RHESSI (Fermi) distribution. A power
function was chosen because the measured RHESSI fluence
distribution could be fairly well fitted with such a function.
The accuracy of the fit will be discussed in section 5. We
interpret the very soft fluence distribution (meaning relatively many low fluence TGFs) from RHESSI to be caused
by dead-time losses that are most significant for high photon
fluxes. Although Fermi also has dead-time losses, the very
hard fluence distribution (meaning relatively many high fluence TGFs) from Fermi can probably be explained by the
long trigger window of 16 ms, which favors high fluence
TGFs. For these reasons we believe that the true fluence
distribution is somewhere in between these two distributions.
[6] The durations of the 591 RHESSI TGFs have a mean
of 374 ms and a median of 299 ms. The duration of a TGF is
defined as the 2s of a Gaussian function fitted to the light
curve of total counts. The majority of the first 53 TGF
pulses measured by Fermi have durations between 100 ms
and 400 ms [Fishman et al., 2011]. For comparison
Gjesteland et al. [2010] reported 5 TGFs measured by
BATSE to have a production duration of 200–250 ms.
3. Differences in Sensitivity and Total Number
of Observed TGFs
[7] For the 591 RHESSI TGFs observed before January 1,
2006 the average time between TGFs was 2.35 day or 0.42
TGFs/day using a lower threshold cut-off of 17 counts
[Grefenstette et al., 2009]. For the first 53 TGFs measured
by Fermi they observed 0.03 TGFs/day when a 16 ms onboard trigger window was applied to the NaI scintillators,
which increased to 0.3 TGFs/day when the same window
was applied to the BGO detectors [Fishman et al., 2011].
However, after the Fermi team started downloading most of
the data obtained over regions where TGFs are produced,
Fishman [2011] reported that more than 1 TGF/day has been
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Figure 2. The average lower threshold of RHESSI (grey)
and FERMI (black) given on the RHESSI scale of counts/
TGF. The distribution of TGFs with an exponent of 2.3 is
shown as a grey curve.
observed. According to Briggs [2011; M. Briggs, personal
communication, 2011] their ground search found 234 TGFs
in 591.8 hours of data over regions which are expected to
have a high TGF rate. Over the same hours and from the
same regions, they found 23 triggered TGFs, a 10.2 times
increase in detection rate. According to Fishman et al.
[2011] 35 TGFs were observed after the trigger algorithm
change (from NaI to BGO) in at least 141 days of data. Of
the 35 triggered TGFs 21 were inside the regions where all
the data have been downloaded [Briggs, 2011] and the
scaling factor of 10.2 should apply. We do not know if this
ratio is also valid for the areas outside the boxes which are
mostly over ocean. Although there are fewer thunderstorms
over ocean the ratio of IC/CG and the fluence distribution of
TGFs might be the same. As we are not aware of any studies
that give any information whether the TGF distribution over
ocean is softer or harder than over land, we will apply an
uncertainty of 50% for the triggered-to-search ratio for the
regions outside the boxes. This uncertainty also accounts for
any seasonal biases in the downloaded data. This gives us a
daily detection rate of 2.5 0.5 TGFs/day (35/141 10.2
and 21/141 10.2 + 14/141 (15.3 or 5.1)).
[8] From the RHESSI data we know that TGFs have a
strong latitudinal dependence with fewer TGFs produced at
higher latitudes. As Fermi, due to its inclination of 25.6
spends more time over regions with more TGFs than
RHESSI (38 inclination), Fermi should see more TGFs than
RHESSI. As we want to derive a relative daily detection rate
that only depends on sensitivity differences we need to correct for this effect. This correction is performed as follows:
First, we consider the RHESSI TGF fluence distribution (NR)
versus latitude (q), dNR/dq, corrected for the latitudinal
cosine effect on area. Then we calculate the fraction of the
orbit RHESSI (OR) spends at various latitudes, dOR/dq, when
the orbit is given as a sine function with amplitude of 38 + 3
latitude. A similar calculation is performed for Fermi,
dOF/dq, but with an amplitude of 25.6 +3 latitude. The
extra 3 is to account for a field of view of about 400 km.
The expected Fermi TGF distribution is then given as
dNF dNR dOF =dq
¼
dq
dq
dOR =dq
ð2Þ
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By integrating dNR/dq and dNF/dq over latitudes we estimate
that Fermi, just due to orbital differences between the two
spacecraft, is expected to see 65% more TGFs than RHESSI.
This means that the relative detection rate between Fermi
and RHESSI due to sensitivity differences only, Y, is given
by (2.5 0.5)/1.65/0.42 = 3.6 0.7. It should be noted that
this is what Fermi would have seen if they downloaded
data similar to RHESSI and is what we will use as the
relative detection rate between the two instruments. However, the real detection rate for Fermi is 1.6 TGFs/day
(21 10.2/141 + 14/141).
[9] Even if the photon flux of a TGF has a rapid rise, the
decay, due to Compton scattering, is usually slow [Østgaard
et al., 2008] and there is no reason to believe that RHESSI,
due to dead-time losses, should miss TGFs with high fluence. Dead-time losses would only lead to underestimating
the fluence of strong TGFs. When Fermi sees more TGFs
than RHESSI it implies that its sensitivity is better. Although
Fermi BGO detectors have a slightly larger effective detector
area than RHESSI, that is 320 cm2 [Meegan et al., 2009;
Briggs et al., 2010] compared to 256 cm2 [Grefenstette
et al., 2009] flying at practically the same altitude, the
most important reason for the higher sensitivity is that a
more efficient trigger algorithm for the on-ground analysis
has been developed for Fermi. According to Briggs [2011]
the on-ground trigger algorithm requires ≥4 counts in each
of the two BGO detector, ≥4 in all the 12 NaI detectors and
with a probability less than 10 11 giving a lower threshold
of 19 counts in all detectors. For the comparison with the
591 RHESSI TGFs for which a lower cut-off threshold of
17 counts (before background subtraction) have been used
we use the ≥8 counts (also before background subtraction) in
the two BGO detectors with an energy averaged effective
detector area of 160 cm2 2 = 320 cm2 to obtain the relative
sensitivity, X, between Fermi and RHESSI as
X ¼
17 320
¼ 2:7
8 256
ð3Þ
This is equivalent to Fermi having a lower threshold of 6.3
on the RHESSI scale as visualized in Figure 2. Although
there are uncertainties related to this estimate we will show
that it provides results that converge with the rest of the
information we have and are consistent with an independent
MC simulation of RHESSI dead-time. Uncertainties related
to the relative sensitivity will be discussed.
4. The True Fluence Distribution and RHESSI
Dead-Time Losses
[10] In the search algorithm to find the 591 RHESSI TGFs
with the daily detection rate of 0.42 TGFs/day a lower
threshold cut-off of 17 counts was used. However, our MC
simulations of dead-time loss indicates that RHESSI only
has a one-to-one response up to 10 counts (see Figure 4a).
However, between 10 and 20 counts the errors of the estimated true counts are still overlapping the one-to-one
response. We will therefore use a fluence of 15 counts as the
threshold where the RHESSI results start to be affected by
dead-time losses, but also show the effect of using 10 and
20 counts.
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With relative sensitivity, X = 2.7, and relative daily detection rate, Y = 3.6 0.7, this can be solved to get an
exponent
l ¼ 2:3 0:2
ð6Þ
Knowing the distribution of TGFs measured by RHESSI,
with l = 3.5 and the estimated true TGF distributions, with
l = 2.3 we can calculate RHESSI dead-time losses as a
function of incoming photons. For a specific number of
TGFs within a fluence interval, dN/dn, in Figure 3a the
dead-time loss is the difference between the true fluence,
nT, and the measured fluence nM divided by nT. This is
shown in Figure 3b where we have used a fluence of 15
(solid line), with 10 and 20 as uncertainties (dotted lines),
Figure 3. (a) The distribution measured by RHESSI (thick
grey) and the estimated true TGF distribution at RHESSI
altitude based on the two instrument’s different photon
detection sensitivities and their relative daily TGF detection
rate. (b) The loss due to dead-time in the RHESSI electronics
as a function of true counts (incoming photon fluence). Solid
line is for 15 counts used as the threshold where RHESSI
experiences dead-time losses. Dotted lines are for lower
threshold of 10 counts (upper) and 20 counts (lower). The
grey cross is the average dead-time loss determined by the
MC simulations described in section 5.
[11] Given that both RHESSI and Fermi are measuring
from a true fluence distribution that follows a power law
with an unknown exponent, l, but with different lower
detection thresholds, we have the following expression for
the total number of TGFs detected by Fermi:
NF ¼
Z
∞
A0 n l dn ¼
n0F
A0
l
1
n10F l
ð4Þ
where n is fluence and n0F is the lower threshold of
detection. The total number of TGFs detected by RHESSI,
NR can be expressed similarly, but with a different lower
threshold, n0R. We can then express the relative total
number of detected TGFs which is equivalent to the relative
daily detection rate, Y, as a function of the two lower
thresholds
Y ¼
NF
n0F
¼ ð Þ1
NR
n0R
l
1
¼ ð Þ1
X
l
ð5Þ
Figure 4. (a) Monte Carlo simulation of the TGF observed
May 2, 2005, with a duration of 361 ms, with increasing true
fluence from 0 to 100. Vertical line denotes the measured
counts and the true counts can be read out from the intersection between MC values and horizontal line, here 45 7.
The diagonal line indicates that RHESSI has no dead-time
losses up to about 15 counts. (b) Grey histogram is the measured fluence distribution of the 591 RHESSI TGFS, while
black histogram is the true fluence distribution running the
MC model on each of the 591 TGFs. Due to background
subtraction there are TGFs with less than 17 counts. The
black, grey and red lines show the fitted power distributions
for the measured (l = 3.5) true (l = 2.6) and the lower bins
of the true (l = 1.7).
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of photons within the duration, which is shown as vertical
lines in Figure 4a. The black horizontal line at 34 counts is
what RHESSI measured for this specific TGF and the true
counts can be read out from the intersection between the MC
values and the horizontal line, here 45 7. This curve would
have been identical to the one shown in Figure 3b if both the
measured counts and duration were equal to the averages, 34
counts and 374 ms. When this MC scheme is applied to all
the 591 RHESSI TGFs a true fluence distribution of TGFs
can be obtained, as shown by the black histogram in
Figure 4b. Using the average fluence of the true distribution
and the measured distribution we get the dead-time losses
for an average RHESSI TGF of 26%, as shown as a grey
cross in Figure 3b. Power functions can be fitted to the distributions. Depending on how many bins from the peak
value that are used for the fit we find that the measured
distribution before dead time correction (grey histogram) can
be fitted with power exponents ranging from 3.2 (11 bins) to
3.7 (17 bins). A c2-test (reduced) of these fits is equally
good (c2R ≤ 0.15). Similarly, for the dead time corrected
distribution (black histogram) we find power exponents
ranging from 2.3 (10 bins) to 3.0 (19 bins), which are
equally good with c2R ≤ 0.2. In Figure 4b we have chosen to
show exponents in the middle of the intervals, l of 3.5 for
the non-corrected distribution, that was used for estimating
the RHESSI dead time losses in section 4. For the corrected
distribution we show a l of 2.6 for the entire distribution and
a l of 1.7 for the lower part, indicating a roll-off, as will be
discussed in section 6.
Figure 5. How the exponent, l, depends on (a) the relative
sensitivity of the two instruments and (b) the relative daily
detection rate. In Figure 5a the vertical line is the relative
sensitivity we have based our calculation on. The dashed
lines show the same dependence when the upper and lower
limits of Y are used. In Figure 5b the solid vertical line is
the relative daily detection rate with lower and upper limits
as dashed lines with the corresponding upper and lower limits for l (horizontal dashed lines). In both panels the dotted
lines are the l for the measured distributions by RHESSI
(grey) and Fermi (black).
as the level where dead-time losses start to affect the
RHESSI counts. The loss for an average TGF (33 counts)
is 24% which is fairly close to what was obtained from
the MC simulations (grey cross), 26% for an average of
35 counts (Figure 4b).
5. Monte Carlo Simulation of RHESSI
Dead-Time Losses
[12] To obtain an independent estimate of RHESSI deadtime losses a MC simulation was performed. For this MC
simulation we used the characteristic times of the RHESSI
electronics [Grefenstette et al., 2009] to determine the deadtime in each of the 8 detectors. Then, for each TGF the
following two steps are performed: 1) The duration of the
TGF is calculated as within 2 standard deviations of a
Gaussian fit to the TGF light-curve. 2) By increasing the
number of photons distributed randomly within the duration
of each TGF a detection efficiency curve is obtained. As this
was performed hundred times for each number of photons
we obtain the statistical error due to the random distribution
6. Discussion
[13] Fermi also has a dead-time loss up to 50% for intense
TGFs [Briggs et al., 2010]. Because Fermi is seeing 3.6 0.7 times more TGFs than RHESSI, we believe that Fermi
due to its more sophisticated search algorithm, is seeing the
weaker part of the TGF fluence distribution. We can not rule
out that Fermi may lose some counts due to dead-time even
for these weak TGFs, but we will argue that the lower
threshold of TGF detection for Fermi is most likely determined by the signal-to-noise ratio rather than dead-time
losses.
[14] There are two important values that our estimated true
fluence distribution depends on: 1) the relative sensitivity
(X) of the two instruments and 2) the relative daily detection
rate (Y), where we have used X = 2.7 and Y = 3.6 0.7. To
examine how uncertainties in these two estimates may
influence our result we can rewrite equation (5) to obtain
l¼1þ
lnðY Þ
lnðX Þ
ð7Þ
[15] In Figure 5a we keep the relative daily TGF detection
rate fixed at Y = 3.6 and let the relative sensitivity (X) vary
from 1 to 5. One can see that if Fermi is more sensitive
relative to RHESSI than we have estimated (moving to
higher values) the true distribution will be slightly harder.
On the other hand, if the two instruments have almost similar
sensitivities the true fluence distribution quickly becomes
very soft. The dashed lines show the same dependence when
the upper and lower limits of Y are used. We have based our
estimate of relative sensitivity on information presented by
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Grefenstette et al. [2009], Meegan et al. [2009], Briggs et al.
[2010], and Briggs [2011, also personal communication,
2011]. For the RHESSI data we have only used the 591
TGFs before the degradation of the instrument occurred. The
average effective detection area is adopted from Briggs et al.
[2010], but looking at Figure 11 of Meegan et al. [2009] one
could argue that the average is closer to 170 cm2. This would
have given us a l of 2.2, but introduces an uncertainty too
small to affect the 0.2 used in equation (6).
[16] In Figure 5b we keep the relative sensitivity fixed at
X = 2.7 and let the daily TGF detection rate (Y) vary from 1
to 6. The daily TGF detection rate for RHESSI is fairly
well established by Grefenstette et al. [2009], while Fermi’s
daily detection rate is given as approximately 1 [Fishman,
2011]. As described above, based on the information
given by Briggs [2011, also personal communication,
2011] we found that the equivalent (to RHESSI) daily
detection rate for Fermi after downloading data, due to
sensitivity differences only, is 1.5 0.3 TGFs/day, with
1.2 (1.8) TGFs/day corresponding to TGFs with higher
(lower) fluence over ocean than land. The grey shaded box
in Figure 5b shows the range spanned by the two extreme
values and indicates that the true fluence distribution of
TGFs as measured from satellite altitude follows a power
law with l = 2.3 0.2. This is in good agreement with the
estimated power distributions with l ranging from 1.9 to
2.5 reported by Gjesteland et al. [2011], using geolocation
and energy spectra of RHESSI TGFs.
[17] The two methods we have used give converging
l-values. Furthermore, if 10 to 12 bins were used for the fit
to dead-time corrected distribution in Figure 4b we would
get l = 2.3. As we in our first approach focus on extending
the distribution down to fluences below the RHESSI lower
threshold, we conclude that both methods support a distribution with l = 2.3 0.2.
[18] What we have estimated is the true TGF distribution
as measured from satellite altitude, which is not necessarily
the same as the true TGF source distribution. Flying much
closer to the source, an experiment like ADELE is probably
exposed to a distribution more similar to the latter. In a
recent paper Carlson et al. [2012] have calculated the relationship between the two and for hard distributions the differences are significant. For a distribution with l = 2.3 0.2
the true source distribution would have l = 2.0 0.2. As
reported by Smith et al. [2011] ADELE, flying at 14 km
altitude, saw only one TGF when passing 1213 lightning
discharges less than 10 km away. However, ADELE was
closer than 4 km to 133 discharges and according to the
model results presented in that paper the sensitivity of
ADELE is increased about two-to-three orders of magnitude
from 10 km to 4 km.
[19] It has been suggested that TGFs are associated with
IC lightning bringing negative charges upward [Cummer
et al., 2005; Williams, 2006; Shao et al., 2010; Cummer
et al., 2011]. As this type of lightning accounts for about
75% of all lightning [Boccippio et al., 2001] this would
imply that almost all lightning discharges have an associated
TGF. We will now discuss this hypothesis in the context of
the power distributions we have found and the non-detection
of TGFs by ADELE as well as the sensitivity of ADELE
versus RHESSI.
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[20] First, we estimate the relative sensitivity between
ADELE at 10 km and RHESSI. We use 400 km as the radius
of the effective detection area below RHESSI [see Collier
et al., 2011, Figure 6] and notice that RHESSI detects
TGFs produced within 38 latitude. Then, the global production rate of TGFs within this latitude range and with
strength larger than the RHESSI threshold of 17 counts is
about 260 TGFs/day. The global lightning rate is 3.8 106/
day [Christian et al., 2003], but within 38 latitude it is
3.5 106/day. If we only consider the IC lightning (75%
of total) we get a RHESSI-TGF/lightning ratio of
9.8 10 5. Of 1213 lightning RHESSI would have seen
0.1 TGF, while ADELE saw 1. Solving equations (5) or (7)
with Y = 10 and l = 2.3 gives X = 6 indicating that ADELE’s
sensitivity at 10 km is about 6 times better than RHESSI
and 2 times better than Fermi. If the source distribution with
l = 2.0 were used these number would be larger.
[21] In Figure 6a we show the integrated distribution of
TGFs, N, as a function of lower detection threshold, n0,
(equation (4)) from 1213 and 133 lightning discharges
assuming that they all make TGFs with a fluence distribution
following a power law with l = 2.0 (solid lines). The two
values of n0 denote the lower threshold (relative scale) for
detecting 1 TGF (N = 1). For l = 2.0 the sensitivity has to
increase by a factor of 10 (1/0.1) to see 1 TGF from a
distribution of 133 given that 1 TGF was detected from a
distribution of 1213. ADELE’s sensitivity is modeled to be
100–1000 times better at 4 km compared to 10 km [Smith
et al., 2011] and corresponds to having a lower threshold
of n0 = 1/100 to 1/1000 (Figure 6a). This would imply that
ADELE should have seen about 10 (at n0 = 1/100) TGFs
from the 133 lightning discharges if they all produce TGFs,
and the probability of non-detection is very low.
[22] It should be noticed that the modeling of ADELE’s
sensitivity is based on certain assumptions. The model is
only valid for IC+ discharges, while at least 50% of the
subset shown in Figure 2 (top and middle) of Smith et al.
[2011] are CG– discharges. A fixed 87 g/cm2 is used for
the avalanche region, which might be reasonable for charge
top below 16 km (3 km charge separation), but is very large
(5 km) for the higher charge tops.
[23] Assuming that ADELE’s sensitivity is indeed 1000
times better at 4 km compared to 10 km our results indicate
that there is a cut-off (or roll-off) in the TGF distribution.
Such a cut-off is implicit in the analysis of a fixed number of
lightning discharges: the lower limit must be chosen such
that the integral of the distribution matches the number of
events. ADELE’s single observation at a relative intensity of
n0 = 1 out of 1213 lightning discharges implies a minimum
intensity threshold of n0 1/1000, the minimum value on
the x axis in Figure 6a. We can estimate at which fluence
value relative to the lower threshold of RHESSI detection
this cut-off might be, assuming that the TGFs follow Poisson
statistics. The probability, p, of non-detection when predicted number of detection is NP, is given by
pN0 ¼ e
NP
ð8Þ
[24] In Figure 6b we show the probability of non-detection
given that one TGF was observed at 10 km as a function of
the relative sensitivity of ADELE between 10 km and 4 km,
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Figure 6. (a) The distribution of TGFs if all the 1213 and
133 lightning discharges can produce TGFs with a power
law distribution with l = 2.0 (solid). The values, n0, indicate
the relative lower threshold for detecting one TGF for l =
2.0 (solid). The vertical dotted line is the highest number
of observed TGFs given a sharp cut-off in the distribution.
The dashed lines are for a power distribution with l = 1.3.
(b) The probability of non-detection as a function of relative
sensitivity for ADELE at 10 km and 4 km given that one
TGF was detected at 10 km. Probabilities are shown for distributions with l = 2.0 (solid) and l = 1.8 and 2.2 (dotted)
and l = 1.3 (dashed). The horizontal dotted line indicates a
probability of 1 out of 10.
given by the relative lower thresholds of detection, n4/n10.
Given that 0.1 (NP = 2.6) from the 133 distribution is a
reasonable probability of non-detection (marked with a
dotted horizontal line in Figure 6b) this cut-off is at a sensitivity level of 5/100 of ADELE at 10 km, which is 5/600 of
the weakest TGF observed by RHESSI (RHESSI has 1/6 of
ADELE sensitivity at 10 km), or 3/600 if one compares
with the average RHESSI TGF, which is a factor of 2 larger
than the RHESSI lower threshold. If the increase of
ADELE’s sensitivity is less than three orders of magnitude
(from 10 km to 4 km) this cut-off would move to lower
values. If all the lightning discharges produces TGFs, the
modeling results of Smith et al. [2011] would have to be off
by a little less than one order of magnitude.
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[25] We can relate this cut-off in the TGF distribution to
the lowest number of electrons that can be produced in a
TGF and what the global TGF production rate would be. Our
modeling results, using the model described by Østgaard
et al. [2008], indicate that the total number of photons produced in an average RHESSI TGF ranges from 1016 (21 km
production altitude) to 1018 (15 km production altitude) in
agreement with others [e.g., Smith et al., 2011]. The probability of bremsstrahlung production increases non-linearly
with energies and is about 10% for 2 MeV electrons [Berger
and Seltzer, 1972] and approaches 100% at higher electron
energies. Measured photon energies >20 MeV indicate that
we are in this energy range, which implies that the number of
electrons is also ranging from 1016 to 1018. With a cut-off in
the TGF distribution at 5/600 of the RHESSI threshold the
lowest possible number of electrons produced in a TGF
would be 1014.
[26] From Figure 6a one can see that a cut-off at n0 =
5/100 which corresponds to 5/100 of ADELE at 10 km and
5/600 of the RHESSI lower threshold would give 20 TGFs
from the 1213 lightnings from which RHESSI would have
seen 0.1 TGF. This implies that the global production rate of
TGFs within 38 latitude is about 200 (20/0.1) times what
we estimated from RHESSI TGF detection. This gives
50000 TGFs/day or about 35 TGFs every minute and compared to the IC lightning occurrence frequency within the
same latitude range of 2.7 106/day, the ratio of TGF/
lightning is about 2%. These numbers are slightly larger
than estimated by Smith et al. [2011].
[27] We should emphasize that these estimates are based
on only one single TGF observation from 10 km. Furthermore, they are based on the assumption of having a sharp
cut-off in the TGF distribution. In reality there is probably a
roll-off which would decrease the lowest number of electrons and increase the global TGF production rate. Our
estimates are consistent with the non-detection by ADELE
and depend strongly on these results. If future aircraft or
balloon missions find slightly different results our estimates
need to be recalculated.
[28] Finally, we will discuss the implication of a roll-off
instead of a sharp cut-off in the TGF distribution which is a
more realistic distribution. Our results indicate that the
power law with l = 2.3 is valid at least down to the Fermi
threshold, which is 1/3 of RHESSI. Looking at the black
histogram in Figure 4b one can argue that there is indeed a
roll-off in the lower 8 bins from the peak value, which can be
fitted with a l of 1.7. According to Carlson et al. [2012],
this corresponds to a source distribution with l < 1.3. As
long as the roll-off threshold is at 1/3 of RHESSI lower
threshold or higher, ADELE is observing from the part of
the distribution with l = 1.3. Such a distribution is shown as
dashed lines in Figure 6a, and one can see that the ADELE’s
sensitivity would have to increase 3 orders of magnitude
(n0 decreases from 107 to 104 on the relative scale) to see
1 TGF from a distribution of 133 TGFs. As can be seen
from Figure 6b the probability of non-detecting at 4 km
(n4/n10 = 1/10000) is only 0.1. In this case we can not rule
out that all IC lightning discharges produce TGFs. Using
the true distribution as seen from space (l = 1.3) an ideal
instrument with sensitivity 10000 times better than
RHESSI would have seen about N = 4000 TGFs/day within
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a radius of 400 km. The lowest number of total electrons
produced in a TGF would then be 1012.
7. Summary
[29] To summarize, we have used two independent methods to find the RHESSI dead-time losses and an estimate of
the true fluence distribution of TGFs as measured from satellite altitude. The two methods give dead-time losses of
24% and 26% for an average RHESSI TGF 33–35 counts.
Assuming a sharp cut-off the true TGF fluence distribution
is found to follow a power law with l = 2.3 0.2 down to
5/600 of the detection threshold of RHESSI. This corresponds to a lowest number of electron produced in a TGF to
be 1014 and a global production rate within 38 latitude
of 50000 TGFs/day or about 35 TGFs every minute, which
is 2% of all IC lightning. If a more realistic distribution with
a roll-off below 1/3 (or higher) of the RHESSI lower
detection threshold with a true distribution with l ≤ 1.7 that
corresponds to a source distribution with l ≤ 1.3 is considered, we can not rule out that all discharges produce TGFs.
In that case the lowest number of total electrons produced in
a TGF is 1012.
[30] Acknowledgments. We are indebted to the RHESSI and Fermi
GBM teams for the design and successful operations of the two missions.
We thank D. A. Smith for the use of RHESSI data and M. Briggs for the
use of Fermi GBM data. This study was supported by the Norwegian
Research Council, under the two contracts 197638/V30 and 208028/F50.
[31] Robert Lysak thanks the reviewers for their assistance in evaluating this paper.
References
Berger, M. J., and S. M. Seltzer (1972), Bremsstrahlung in the atmosphere,
J. Atmos. Terr. Phys., 34, 85–108.
Boccippio, D. J., K. L. Cummings, H. J. Christian, and S. J. Goodman
(2001), Combined satellite- and surface-based estimation of the intracloud-cloud-to-ground lightning ratio over the continental United States,
Mon. Weather Rev., 129(1), 108–122, doi:10.1175/1520–0493(2001)129.
Briggs, M. S. (2011), More TGFs from GBM, paper presented at Terrestrial
Gamma-Ray Flash Workshop 2011, Cent. for Space Plasma and Aeron.
Res., Univ. of Ala., Huntsville.
Briggs, M. S., et al. (2010), First results on terrestrial gamma ray flashes
from the Fermi Gamma-ray Burst Monitor, J. Geophys. Res., 115,
A07323, doi:10.1029/2009JA015242.
Briggs, M. S., et al. (2011), Electron-positron beams from terrestrial lightning observed with Fermi GBM, Geophys. Res. Lett., 38, L02808,
doi:10.1029/2010GL046259.
Carlson, B. E., N. G. Lehtinen, and U. S. Inan (2007), Constraints on terrestrial gamma ray flash production from satellite observation, Geophys.
Res. Lett., 34, L08809, doi:10.1029/2006GL029229.
Carlson, B. E., T. Gjesteland, and N. Østgaard (2012), Connecting the terrestrial gamma-ray flash source strength and observed fluence distributions, J. Geophys. Res., 117, A01314, doi:10.1029/2011JA017122.
Christian, H. J., et al. (2003), Global frequency and distribution of lightning
as observed from space by the Optical Transient Detector, J. Geophys.
Res., 108(D1), 4005, doi:10.1029/2002JD002347.
Collier, A. B., T. Gjesteland, and N. Østgaard (2011), Assessing the power
law distribution of TGFs, J. Geophys. Res., 116, A10320, doi:10.1029/
2011JA016612.
A03327
Cummer, S. A., Y. Zhai, W. Hu, D. M. Smith, L. I. Lopez, and M. A. Stanley
(2005), Measurements and implications of the relationship between lightning and terrestrial gamma ray flashes, Geophys. Res. Lett., 32, L08811,
doi:10.1029/2005GL022778.
Cummer, S. A., G. Lu, M. S. Briggs, V. Connaughton, S. Xiong, G. J. Fishman,
and J. R. Dwyer (2011), The lightning-TGF relationship on microsecond
timescales, Geophys. Res. Lett., 38, L14810, doi:10.1029/2011GL048099.
Dwyer, J. R., and D. M. Smith (2005), A comparison between Monte Carlo
simulations of runaway breakdown and terrestrial gamma-ray flash observations, Geophys. Res. Lett., 32, L22804, doi:10.1029/2005GL023848.
Dwyer, J. R., et al. (2004), A ground level gamma-ray burst observed in
association with rocket-triggered lightning, Geophys. Res. Lett., 31,
L05119, doi:10.1029/2003GL018771.
Dwyer, J. R., et al. (2005), X-ray bursts associated with leader steps
in cloud-to-ground lightning, Geophys. Res. Lett., 32, L01803,
doi:10.1029/2004GL021782.
Dwyer, J. R., B. W. Grefenstette, and D. M. Smith (2008), High-energy
electron beams launched into space by thunderstorms, Geophys. Res.
Lett., 35, L02815, doi:10.1029/2007GL032430.
Fishman, G. J. (2011), Positrons observed to originate from thunderstorms,
Eos Trans. AGU, 92(22), 185, doi:10.1029/2011EO220001.
Fishman, G. J., et al. (1994), Discovery of intense gamma-ray flashes of
atmospheric origin, Science, 164, 1313–1316.
Fishman, G. J., et al. (2011), Temporal properties of the terrestrial gammaray flashes from the Gamma-Ray Burst Monitor on the Fermi Observatory, J. Geophys. Res., 116, A07304, doi:10.1029/2010JA016084.
Gjesteland, T., N. Østgaard, J. Stadsnes, P. H. Connell, and G. J. Fishman
(2010), Effects of deadtime losses on terrestrial gamma ray flash
measurements done by the Burst And Transient Source Experiment,
J. Geophys. Res., 115, A05303, doi:10.1029/2009JA014754.
Gjesteland, T., N. Østgaard, A. B. Collier, B. E. Carlson, M. B. Cohen,
and N. G. Lehtinen (2011), Confining the angular distribution of terrestrial gamma ray flash emission, J. Geophys. Res., 116, A11313,
doi:10.1029/2011JA016716.
Grefenstette, B. W., D. M. Smith, B. J. Hazelton, and L. I. Lopez (2009),
First RHESSI terestrial gamma ray flash catalog, J. Geophys. Res., 114,
A02314, doi:10.1029/2008JA013721.
Gurevich, A. V., G. M. Milikh, and R. Roussel-Dupré (1992), Runaway
electron mechanism of air breakdown and preconditioning during a thunderstorm, Phys. Lett. A, 165(5), 463–468.
Meegan, C. A., et al. (2009), The Fermi Gamma-ray Burst Monitor, Astrophys. J., 702, 791–804, doi:10.1088/0004–637X/702/1/791.
Nemiroff, R. J., J. T. Bonnell, and J. P. Norris (1997), Temporal and spectral characteristics of terrestrial gamma flashes, J. Geophys. Res., 102
(A5), 9659–9665.
Nguyen, C. V., A. P. J. van Deursen, and U. Ebert (2008), Multiple X-ray
bursts from long discharges in air, J. Phys. D Appl. Phys, 41, 234012,
doi:10.1088/0022–3727/41/23/234012.
Østgaard, N., T. Gjesteland, J. Stadsnes, P. H. Connell, and B. Carlson
(2008), Production altitude and time delays of the terrestrial gamma
flashes: Revisiting the Burst and Transient Source Experiment spectra,
J. Geophys. Res., 113, A02307, doi:10.1029/2007JA012618.
Shao, X. M., T. Hamlin, and D. M. Smith (2010), A closer examination of
terrestrial gamma-ray flash-related lightning processes, J. Geophys. Res.,
115, A00E30, doi:10.1029/2009JA014835.
Smith, D. M., et al. (2011), The rarity of terrestrial gamma-ray flashes,
Geophys. Res. Lett., 38, L08807, doi:10.1029/2011GL046875.
Williams, E. R. (2006), Problems in lightning physics—the role of polarity
asymmetry, Plasma Sources Sci. Technol., 15(2), 91–108, doi:10.1088/
0963-0252/15/2/S12.
B. Carlson, T. Gjesteland, R. S. Hansen, and N. Østgaard, Department of
Physics and Technology, University of Bergen, Allegt. 55, N-5007 Bergen,
Norway. ([email protected])
A. B. Collier, SANSA Space Science, Hospital Street, Hermanus, 7200
South Africa.
8 of 8
Paper 2
6.2 How simulated fluence of photons from terrestrial gamma ray
flashes at aircraft and balloon altitudes depends on initial parameters
R. S. Hansen, N. Østgaard, T. Gjesteland, and B. Carlson
Journal of Geophysical Research Space Physics, 118, doi:10.1002/jgra.50143, 2013
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6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and
balloon altitudes depends on initial parameters
81
JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 1–7, doi:10.1002/jgra.50143, 2013
How simulated fluence of photons from terrestrial gamma ray flashes
at aircraft and balloon altitudes depends on initial parameters
R. S. Hansen,1,2 N. Østgaard,1,2 T. Gjesteland,1,2 and B. Carlson1,2
Received 8 August 2012; revised 21 November 2012; accepted 24 January 2013.
[1] Up to a few years ago, terrestrial gamma ray flashes (TGFs) were only observed by
spaceborne instruments. The aircraft campaign ADELE was able to observe one TGF,
and more attempts on aircraft observations are planned. There is also a planned campaign
with stratospheric balloons, COBRAT. In this context an important question that arises is
what count rates we can expect and how these estimates are affected by the initial
properties of the TGFs. Based on simulations of photon propagation in air we find the
photon fluence at different observation points at aircraft and balloon altitudes. The
observed fluence is highly affected by the initial parameters of the simulated TGFs. One
of the most important parameters is the number of initial photons in a TGF. In this paper,
we give a semi-analytical approach to find the initial number of photons with an order of
magnitude accuracy. The resulting number varies over several orders of magnitude,
depending mostly on the production altitude of the TGF. The initial production altitude is
also one of the main parameters in the simulations. Given the same number of initial
photons, the fluence at aircraft and balloon altitude from a TGF produced at 10 km
altitude is 2–3 orders of magnitude smaller then a TGF originating from 20 km altitude.
Other important parameters are altitude distribution, angular distribution and amount of
feedback. The differences in altitude, altitude distribution and amount of feedback are
especially important for the fluence of photons observed at altitudes less than 20 km, and
for instruments with a low-energy threshold larger than 100 keV. We find that the
maximum radius of observation in 14 km for a TGF with the intensity of an average
RHESSI TGF is smaller than the results reported by Smith et al. (2011), and our results
support the conclusion in Gjesteland et al. (2012) and Østgaard et al. (2012) that TGFs
probably are a more common phenomenon than previously reported.
Citation: Hansen, R. S., N. Østgaard, T. Gjesteland, and B. Carlson (2013), How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters, J. Geophys. Res. Space Physics, 118,
doi:10.1002/jgra.50143.
1. Introduction
[3] From spectral analyses of the TGFs seen from space,
TGFs have been found to have production altitudes between
15 and 20 km [Dwyer and Smith, 2005; Gjesteland et al.,
2010]. There might be TGFs produced at lower altitudes, but
due to atmospheric attenuation they will not be detectable
from space. Dwyer and Smith [2005] showed that an
average RHESSI TGF could be fairly accurately modeled by assuming 1017 initial photons produced at
15 km altitude. Østgaard et al. [2012] have suggested
that there might exist TGFs with intensities down to 1012
initial photons.
[4] Several studies have also aimed at finding the initial
angular distribution of the photons in a TGF. Gjesteland
et al. [2011] used TGF and lightning observations together
with simulations and found the observations to be consistent
with an isotropic angular distribution inside a cone with half
angle between 30° and 40°. Hazelton et al. [2009] used an
anisotropic angular distribution out to 90 degrees and found
the best fit to be for a beam with a half maximum at 35° (read
out from Figure 2b of Hazelton et al. [2009]).
[2] Terrestrial gamma ray flashes (TGFs) are short bursts
of high energy radiation originating from the Earth’s
atmosphere and observed from space. The radiation is produced, through the bremsstrahlung process, by energetic
electrons that are accelerated by relativistic runaway electrons in strong electric fields. The TGFs are found to be
closely connected to thunderstorms and lightning discharges
[Inan et al., 1996; Cohen et al., 2010; Shao et al., 2010],
so the electric fields are expected to be located in or
around thunderstorms.
1
Department of Physics and Technology, University of Bergen, Bergen,
Norway.
2
Birkeland Centre for Space Science, N-5020 Bergen, Norway
Corresponding author: R. S. Hansen, Department of Physics and Technology, Allegt. 55, N-5007, Bergen, Norway. ([email protected])
©2013. American Geophysical Union. All Rights Reserved.
2169-9380/13/10.1002/jgra.50143
1
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HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES
13
[5] So far, most observations of TGFs have been
obtained by spaceborne instruments. The first observations were made by the Burst and Transient Source
experiment (BATSE) on board the Compton Gamma Ray
Observatory (CGRO) [Fishman, 1994]. During the last
10 years, observations have also been made by Reuven
Ramaty High Energy Solar Spectroscopic Imager (RHESSI)
[Smith et al., 2005], FERMI [Briggs, 2010], and AGILE
[Marisaldi, 2010].
[6] In 2009, an effort to observe TGFs using aircraftborne instruments was carried out [Smith, 2011a]. During
37 hrs of observations the ADELE instrument detected only
one event [Smith, 2011b]. During the flight time, there were
more than 1000 lightning discharges closer than 10 km from
the aircraft. Smith [2011a] also made a simulation and calculation of the expected number of TGFs. Due to the very
few detected events, they concluded that only 0.1–1% of all
flashes produce TGFs and that the TGF intensities cannot
follow a power law distribution below 1/100 of the average
RHESSI TGFs. However, a recent study by Østgaard et al.
[2012] based on Fermi and RHESSI TGFs as well as the
non-detection by ADELE argued that one cannot rule out
that all lightning produce TGFs. This is also supported by
the findings of more TGFs in the RHESSI data [Gjesteland
et al., 2012] and in the GBM Fermi data [Østgaard
et al., 2012].
[7] In this paper, we show the results of a simulation
of photon fluence at aircraft altitudes as well as at balloon
altitudes. As should be clear from this introduction, the constraints obtained from observations still open up for a broad
variation of initial conditions, and we show that the resulting
fluence is highly dependent on these initial conditions. We
also show that the number of initial photons in a TGF seen
from space is dependent on the initial conditions used in
the simulation.
Altitude [km]
12
11
10
9
0.0
0.2
0.4
0.6
0.8
1.0
Relative number of photons/km
Figure 1. The altitude distribution from Smith [2011a]
shown for an initial production altitude of 12 km. The photons are distributed over an atmospheric depth of 87 g/cm2 .
spectrum one can get from bremsstrahlung and the cutoff
corresponds to the largest single photon energy observed
by AGILE [Marisaldi, 2010]. Tavani [2011] claim to have
observed photons with energies up to 100 MeV, but the number of photons with these energies is very small. As the
expected production altitude of TGFs is below 20 km, we
have used initial production altitudes between 8 and 20 km.
To be able to compare with earlier modeling results, we
have also used both discrete and distributed photon production altitude distributions. For the distributed altitudes, we
have used the distribution described in Smith [2011a] where
the avalanche region extends over 87 g/cm2 of air. Figure 1
shows the altitude distribution for a production altitude of
12 km and is taken directly from Smith [2011a]. For other
altitudes, this distribution is scaled to stretch over 87 g/cm2
at that specific altitude with the maximum of the distribution at the altitude in question. This means that the vertical
length of the distribution is large for large initial altitudes
and smaller for low initial altitudes. The distributed altitudes
will be discussed below and our results will be compared
with the results of Smith [2011a].
[10] We use three different angular distributions: (1) all
photons distributed isotropically within a cone of ˙30° half
angle, (2) distributed isotropically within ˙40° half angle,
and (3) angular distributions out to 90° as shown in Figure
2a of Hazelton et al. [2009], all centered around the vertical direction. The angular distribution of Hazelton et al.
[2009] was obtained from a model of the RREA with a
vertical electric field and gave an energy-dependent angular distribution. For photons with energy less than 1 MeV,
we have used the red distribution shown in Figure 2a of
Hazelton et al. [2009]; for photons with energy more than
1 MeV, we have used the blue distribution in the same
figure. Gjesteland et al. [2011] found all of these angular
2. Monte Carlo Simulations
[8] The simulation used to find the expected detection
rates is based on the Monte Carlo model developed by
Østgaard et al. [2008]. This model is a more simple model
than for instance GEANT or the model of Dwyer [2012], but
Østgaard et al. [2008] found good correspondence between
this model and GEANT. The model propagates photons
through the atmosphere in length steps. The density of the
atmosphere is approximated by an exponential fit to MSIS
data. The initial photons are given an initial energy (E),
altitude, and direction and are propagated through the atmosphere. The model takes Compton scattering, photoelectric
absorption, and pair production into account. The Compton
electrons are not taken into account, the photons produced by
bremsstrahlung from the electron and positron after pair production is not taken into account, and the positron is assumed
to annihilate at the same position as the production of the
positron. Østgaard et al. [2008] showed that this simplification gives about 7% less photons, in the energy range below
80 keV. As the lower energy threshold for instruments is typically in the range from 200 to 400 keV, the simplification
will not affect our results significantly.
[9] We have used 100 million initial photons with an initial energy spectrum as a 1/E spectrum with a cutoff at
40 MeV for all simulations. This is the hardest energy
2
6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and
balloon altitudes depends on initial parameters
83
HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES
NI =
R m
I( )dA( )
R m
0 dA( )
0
(1)
where I is the fluence at a given angle , dA is a small annular
area at the angle , and m is the maximum angle of observation. If we assume an isotropic initial angular distribution,
the fluence is given as
I( ) =
kI0
d2
(2)
where I0 is the initial number of photons per steradian,
d = h/ cos as shown in Figure 3, and k is a factor to account
for the loss of photons in the atmosphere. From the geometry
of the calculation shown in Figure 3, we get
dA = 2ada = 2h2
tan d
cos2 (3)
Solving these equations for I0 , we get
Figure 2. The geometry for the simulations. Horizontal
radius is the distance from the initial photon production.
I0 =
R
sin NIh2 0m cos
3 d
R m
k
tan d
(4)
0
distributions to be consistent with observations. The photons going downward due to the feedback process described
in Dwyer [2007, 2012] have been approximated by sending 0% (no feedback), 0.1% (weak feedback), or 1% (strong
feedback) of the initial photons downward with the same
initial angular distribution as the photons going upward.
The fraction of photons initially traveling downward is
determined by using the average number of downward traveling positrons produced per runaway electrons found by
Dwyer [2012]. The number is found to be 3 10–4 rn positrons per runaway electron per meter, where rn is
the number density of air relative to the ground. With
electric field strengths just above the runaway threshold,
around 30% of these positrons will turn around and be
accelerated downward in the electric field [Dwyer, 2012,
Figure B3]. The vertical field size needed to get an average RHESSI TGF is found by Dwyer and Smith [2005]
to be of the order of 100 m/rn . These numbers give
about 1% photons initially traveling downward. The fraction of about 1% is also consistent with strong feedback in
Figure 1 in Babich [2005].
[11] We have sampled all photons passing through detection altitudes of 14, 20 (aircraft altitudes), and 35 km (balloon altitude) and sorted them in intervals of 1 km horizontal
radius from the initial position. The geometry is shown in
Figure 2. The number of photons are then scaled according
to the number of initial photons assumed.
The total initial number of photons is then found by multiplying this with the solid angle:
N0 = I0 2(1 – cos m )
(5)
[13] The factor k is calculated from the Monte Carlo
results as the relative number between the number of photons escaping the atmosphere to the number of initial photons. For each choice of initial parameters, we get a different
k. The initial altitude distribution and the initial photon
angular distribution give some contribution, but the main
parameter is the production altitude. As we are only trying
to determine the order of magnitude of k, we neglect other
contributions than the initial production altitude. The values
of k are in the range between 10–2 and 10–4 for altitudes from
20 km to 10 km. By using a discrete initial altitude distribution and the initial photon angular distribution of Hazelton
et al. [2009, Figure 2a], we get a number of photons as given
in Table 1.
3. Number of Initial Photons
[12] The number of initial photons in an average RHESSI
TGF can be calculated semi-analytically. The average TGF
detected by RHESSI has a fluence of NI = 0.1 photons/cm2
and RHESSI has been shown to see TGFs at least out to 600
km away from nadir [Cohen et al., 2010; Gjesteland et al.,
2011; Collier et al., 2011]. The average fluence of photons
in a circular area can be expressed as
Figure 3. The geometry used for the calculation of number
of initial photons. d is the distance between the initial photon
production and the satellite, h is the difference in altitude
between the initial photon production and the satellite, and
is the angle between h and d.
3
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HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES
Table 1. Number of Initial Photons for Different Initial Production Altitudes
Initial Photon Altitude
Number of Initial Photons
10 km
15 km
20 km
1018
1017
1016
[14] As seen in Table 1, the initial production altitude gives a large variation in the number of initial photons needed to match the average intensities observed by
RHESSI. These numbers are calculated with m = 45°, and
the result is sensitive to the choice of this parameter. TGFs
have been observed out to m = 60° [Cohen et al., 2010]
but the small number of TGFs at these large angles may
suggest that these TGFs are especially strong. If we use
m = 60°, the number of initial photons increase with a
factor of 2–3. When using a distributed initial production
altitude distribution, the number of initial photons increases
by approximately 10%. A change in the initial photon angular distribution gives an increase of up to 20%, while varying
the production altitude gives variations of a factor of 10
and 100.
Figure 5. Fluence of photons at 20 km altitude. The detection threshold is set to 300 keV, the initial number of photons
is 1017 , and the initial photon altitude distribution is discrete.
some will be at the same altitude or above. The fluence of
photons is then highly dependent on the other initial conditions. Figure 4 also shows how the fluence varies with initial
angular distribution. As long as the observation altitude is
higher than the initial production altitude, the main difference between the initial angular distributions is that the two
isotropic distributions give a clear drop in fluence around the
maximum angle of 30° or 40°. This is an effect of observing
inside or outside the initial cone of the photon angular distribution. When the photons are distributed smoothly out to
90°, there is no such cutoff. For horizontal distances larger
than where we see the drop off distance, the fluence for all
angular distributions is similar.
[17] As long as the TGFs are observed above the initial
production altitude, the fluence does not depend significantly
on the initial production altitude distribution (not shown).
For isotropic initial angular photon distribution, the drop at
30° or 40° half angle is sharper for a discrete initial production altitude than for a distributed initial production altitude.
The effect of feedback is also small for observational altitudes higher than the initial production altitude.
[18] Figure 5 is fluence for observation at 20 km altitude
and shows the same features as commented in connection
to observations at 35 km altitudes. For production at 20 km
altitude (black curve), we see that the differences between
the initial photon angular distributions are small. Hence, the
number of backscattered photons is quite similar for the
three different cases.
[19] Figure 6 shows the fluence of photons at 14 km.
Observations at this altitude show a large difference between
observations above or below the initial production altitude
of the TGF. The photons below the initial production altitudes consist of photons being Compton scattered down and
photons produced by positrons moving down. In the process of Compton scattering, the photons will in general lose
much of their energy. As seen in the figure, the fluence from
a TGF produced at 20 km is much smaller than for production closer to the observational altitude. Here, the solid
lines are for production at discrete altitude and the dashed
lines are for distributed initial altitudes. A distributed initial production altitude gives a slightly larger fluence when
the observations are made below the initial production altitude. This will be discussed below. The difference between
4. Dependence on Initial Conditions
[15] For the simulations presented in the beginning of this
section, we have used an initial number of photons of 1017 ,
of which 108 are simulated and then scaled with 109 . This
corresponds to a production altitude of 15 km for an average
RHESSI TGF and is the most used number of initial photons in other models [Dwyer, 2012]. The results when using
different number of initial photons for the different initial
altitudes are shown at the end of the section.
[16] The initial production altitude of the photons is very
important due to the attenuation in the dense lower atmosphere. As shown in Figure 4, the difference in fluence when
observed at 35 km varies 2–3 orders of magnitude when
assuming production altitudes from 10 km to 20 km. For
observations at 14 km and 20 km, some of the initial production altitudes will be below the observation altitude and
Figure 4. Fluence of photons at 35 km altitude. The detection threshold is set to 300 keV, the initial number of photons
is 1017 , and the initial photon altitude distribution is discrete.
The drop in the two isotropic angular distributions is due to
the effect of being inside or outside of the initial cone.
4
6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and
balloon altitudes depends on initial parameters
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HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES
Table 2. Maximum Radius of Detection of All the Various
TGFs Modeled in This Worka
Detection Altitude
14 km
20 km
35 km
Unscaled
300 keV 100 keV
6 km
14 km
27 km
8 km
19 km
32 km
Scaled
300 keV 100 keV
3 km
18 km
39 km
6 km
23 km
51 km
a
Unscaled is maximum radius for a TGF with 1017 initial photons at
all altitudes, scaled is for TGFs initial number of photons scaled according to Table 1. The maximum radius is given for instruments with a low
energy threshold of 100 keV and 300 keV.
main part of the observed photons is backscattered photons
originally directed upward. This makes the intensity difference between TGFs with and without feedback very small at
radial distances larger than about 1 km.
[22] What mostly affects the ability to detect TGFs at
different observational altitudes is the maximum horizontal
distance of detection. Table 2 shows the maximum horizontal distance from the source at which the instrument can still
detect all the various TGFs, independent of initial conditions, within the constraints of this paper. In other words, we
have used the initial conditions that give the smallest fluence
at the observational altitude in consideration. The instrument
is assumed to have a detection limit of 0.1 photon/cm2 . With
an energy threshold of 300 keV, the instrument can detect
all the various TGFs within a radial distance of 27 km when
observed at 35 km altitude. At 20 km altitude, the maximum
radial distance is 14 km, and at 14 km altitude maximum
distance is 6 km.
[23] Another major difference is the change between
observing the TGF from a position above or below the altitude where the TGF originates. When observed at 14 km
altitude, the probability of detection is highly affected by the
amount of feedback and the altitude distribution of the initial
photons. The fluence of photons is much smaller with no or
weak feedback (0.1%), than with an average feedback (1%)
or more, which also makes the maximum radius of detection
much smaller. This is further discussed below.
[24] With a decreasing lower energy threshold from
E > 300 keV to E > 100 keV, the fluence and the maximum radial distance of detection increase. This is shown in
Table 2. The increased number of photons is most important at large radial distances where the relative number of
low energy photons to high energy photons is largest. When
the photons are distributed out to 30° or 40°, all photons
detected at large angles/large horizontal distance have experienced Compton scattering and lost energy [Østgaard et al.,
2008; Hazelton et al., 2009]. Thus, we see a larger number
of high energy photons at large distances when the photons
are distributed out to 90°
4.1. Differentiated Number of Initial Photons
[25] Table 2 and Figure 8 show the maximum radius of
observation and fluence at 35 km altitude when we use 1016
initial photons for a TGF originating at 20 km altitude, 1017
initial photons for a TGF produced at 15 km altitude, and
1018 initial photons for a TGF produced at 10 km altitude.
Figure 8 shows that the fluence of photons is about similar
when using differentiated number of initial photons. This is
because the number of photons is calculated to match the
average RHESSI TGF, and the fluence of photons at a given
Figure 6. Fluence of photons at 14 km altitude. The detection threshold is 300 keV, the initial number of photons is
1017 , and the photons have an initial angular distribution out
to 90°. The TGFs with distributed altitudes are distributed
according to Figure 1.
distributed and discreet altitudes for TGFs produced at 10
km and 15 km is small. This is because the distributed altitudes have a very narrow peak which means that the main
part of the photons are originating close to the maximum
altitude of the distribution.
[20] Figure 7 shows the effect of feedback when the observations are made below the initial production altitude. At
these observational altitudes, even a small feedback will give
a larger fluence than with no feedback, and an increased
feedback will increase the fluence significantly. The fluence
falls off somewhat faster with radial distance when feedback is included. All the profiles are for discrete production
altitudes, and the differences are larger for discrete altitudes
than for distributed altitudes.
[21] When observing from below the production altitude,
the drop at 30° or 40° half angles is only seen when feedback is included. This is an effect of using the same initial
photon angular distributions for photons going downward
and upward. For the TGF originating at 15 km altitude, the
Figure 7. Fluence of photons at 14 km altitude. The detection threshold is 300 keV, the initial number of photons is
1017 , the photons have an initial angular distribution out to
90°, and the initial photon altitude distribution is discrete.
Feedback is approximated by giving 1% of the photons an
initial downward direction, see section 5 for discussion.
5
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et al. [2005] show the existence of electric fields larger than
the limit for relativistic breakdown only extend over 1 km
at 6 km altitude. This corresponds to an atmospheric depth
of 70 g/cm, which is comparable to a 5 km vertical extension
of the electric field at 20 km altitude. In balloon observations
reported by Stolzenburg et al. [2007], from several observations at higher altitudes, the electric field seems to extend
over even smaller vertical distances.
[27] Having electric fields at the threshold for RREA over
an atmospheric depth of 87g/cm2 implies a potential difference of 200 MV for any altitude. This is the lower limit
for the production of high energy photons across the whole
vertical distance used as the distributed altitudes in our modeling. From balloon soundings, the potential between the
nearest relative maximum and minimum potential in thunderclouds was reported by Marshall and Stolzenburg [2001]
to be up to 132 ˙ 2 MV. Most thunderclouds are therefore
not expected to have potentials of more than 200 MV which
is required for RREA over 87 g/cm2 . As the altitude distribution in Smith [2011a] is derived from the assumption
of a very powerful thunderstorm, they probably overestimate the feedback factor as well as the prediction of seeing
TGFs by letting the photons being produced over a too large
altitude range.
[28] A consequence of having electric fields over large
vertical distances is that at least 10% of the photons
will have initial production altitudes lower than 15 km
for all the different initial altitudes. This also explains
the difference between discrete and distributed initial production altitudes for observations in 14 km altitude in
our results.
[29] Figure 9 shows a comparison between our results and
Figure 1 in Smith [2011a]. The figure of Smith [2011a] gives
the contours for 20, 200, 2000, and 20,000 counts in the
detector used by ADELE. We have not been able to propagate out photons through the aircraft body, which means
that we overestimate the number of photons. We have used
an effective area of the detector of 65 cm2 [Smith, 2011a].
Figure 8. Fluence of photons at 35 km altitude. The detection threshold is set to 300 keV and the initial photon altitude
distribution is discrete. The number of initial photons is
scaled according to Table 1.
altitude should then be the same for all initial production
altitudes. If we had used the exact number from the calculation, instead of order of magnitude, all three curves should be
equal. This also underlines that the number of initial photons
is an important parameter for simulations of TGFs and that
the production altitude is the main parameter determining
the final flux.
5. Discussion
[26] To compare our results with the results of
Smith [2011a], we have distributed the initial photons over
87 g/cm2 of atmosphere. At 8 km altitude, this corresponds
to a vertical distance of 1500 m. Due to the exponential
decrease in density of the atmosphere with altitude, this vertical distance will increase for higher altitudes. At 20 km
altitude, the photons are distributed over 5800 m vertical distance with the top of the distribution at 20 km. Using balloon
measurements of electric fields in thunderstorms, Marshall
Figure 9. Contours of counts in the detector used by ADELE [Smith, 2011a]. The black curves are
results from Smith [2011a], and the gray curves are our results including error bars. The left figure shows
our results without feedback and the right figure is with 1% feedback. The curves are for an observational
altitude of 14 km, with initial production altitudes distributed over 87 g/cm2 and initial production angles
out to 90°.
6
6.2 How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and
balloon altitudes depends on initial parameters
87
HANSEN ET AL.: FLUENCE OF PHOTONS FROM TGFS AT AIRCRAFT AND BALLOON ALTITUDES
References
In Figure 9, the results of Smith [2011a] are shown in black
and our results are shown in gray with error bars. As we calculate the flux of photons at every kilometer radius, we will
have an error of ˙1 km. The figure on the left shows our
results without feedback and the figure to the right shows the
results with 1% feedback. Without feedback, our contours
drop faster to 0 radius at high production altitudes compared
to Smith [2011a]. With 1% feedback, the curves are more
similar, but we have to include 5% feedback to be able to
replicate the shape of the contours from Smith [2011a]. However, we are not able to replicate the distances that are shown
by Smith [2011a]. The main difference in our simulations
and the simulations of Smith [2011a] is the energy-angle
distribution. We assumed the same energy distribution for
the downward running photons produced by feedback as
the upward moving photons. Then we have implemented
the energy-dependent angular distribution of Hazelton
et al. [2009] by distributing all energies >1 MeV according
to Figure 2a in Hazelton et al. [2009], but have neglected
that the high energy part of the photon spectrum has a narrower angular distribution. Hence, the high energy photons
in our model is distributed more widely than is the case in
Hazelton et al. [2009] and Smith [2011a]. This results
in a small bias toward larger observational distances in
our results.
[30] The results in this paper are based on the intensities of an average TGF. However, according to Østgaard
et al. [2012], one can expect a large number of TGFs with
lower initial intensity. For these TGFs, the maximum radius
of detection will be even smaller. ADELE had 133 discharges closer than 4 km to the aircraft. The results of our
simulations show that if the assumptions made by Smith
[2011a] are valid then the non-detection of ADELE means
that TGFs are rare events. However, if the TGFs are produced in a shorter altitude interval and with less feedback,
or with lower intensities than an average RHESSI TGF, then
the TGFs might not be detectable to ADELE even at small
radial distances. The results presented here combined with
the fluence distribution found by Østgaard et al. [2012]
makes it very likely that all the 133 discharges closer than
4 km from ADELE were low fluence TGFs that did not produce detectable signal for ADELE. Furthermore, our results
support the conclusion by Gjesteland et al. [2012] and
Østgaard et al. [2012] that TGFs probably are a more
common phenomenon than previously reported.
Babich, L. P. (2005), The feedback mechanism of runaway air breakdown,
Geophys. Res. Lett., 32(9), 1–5, doi:10.1029/2004GL021744.
Briggs, M. S., et al. (2010), First results on terrestrial gamma ray flashes
from the Fermi gamma-ray burst monitor, J. Geophys. Res., 115(A7),
1–14, doi:10.1029/2009JA015242.
Cohen, M. B., U. S. Inan, R. K. Said, and T. Gjestland (2010), Geolocation of terrestrial gamma-ray flash source lightning, Geophys. Res. Lett.,
37(2), 1–5, doi:10.1029/2009GL041753.
Collier, A. B., T. Gjesteland, and N. Østgaard (2011), Assessing the power
law distribution of TGFs, J. Geophys. Res., 116(A10), A10,320, doi:
10.1029/2011JA016612.
Dwyer, J. R. (2007), Relativistic breakdown in planetary atmospheres,
Phys. Plasmas, 14(4), 042,901, doi:10.1063/1.2709652.
Dwyer, J. R. (2012), The relativistic feedback discharge model of terrestrial gamma ray flashes, J. Geophys. Res., 117(A2), A02,308, doi:
10.1029/2011JA017160.
Dwyer, J. R., and D. M. Smith (2005), A comparison between Monte
Carlo simulations of runaway breakdown and terrestrial gamma-ray
flash observations, Geophys. Res. Lett., 32(22), 1–4, doi: 10.1029/
2005GL023848.
Fishman, A. G. J., et al. (1994), Discovery of intense gamma-ray flashes of
atmospheric origin, Adv. Sci., 264(5163), 1313–1316.
Gjesteland, T., N. Østgaard, P. H. Connell, J. Stadsnes, and G. J. Fishman
(2010), Effects of dead time losses on terrestrial gamma ray flash measurements with the burst and transient source experiment, J. Geophys.
Res., 115, 1–10, doi:10.1029/2009JA014578.
Gjesteland, T., N. Østgaard, A. B. Collier, B. E. Carlson, M. B. Cohen, and
N. G. Lehtinen (2011), Confining the angular distribution of terrestrial
gamma-ray flash emission, J. Geophys. Res., 116(A11), A11,313, doi:
10.1029/2011JA016716.
Gjesteland, T., N. Østgaard, A. B. Collier, B. E. Carlson, C. Eyles, and
D. M. Smith (2012), A new method reveals more TGFs in the RHESSI
data, Geophys. Res. Lett., 39(5), 1–5, doi:10.1029/2012GL050899.
Hazelton, B. J., B. W. Grefenstette, D. M. Smith, J. R. Dwyer, X.-M. Shao,
S. A. Cummer, T. Chronis, E. H. Lay, and R. H. Holzworth (2009),
Spectral dependence of terrestrial gamma-ray flashes on source distance,
Geophys. Res. Lett., 36(1), 1–5, doi:10.1029/2008GL035906.
Inan, U. S., S. C. Reising, G. J. Fishman, and J. M. Horack (1996),
On the association of terrestrial gamma-ray bursts with lightning and
implications for sprites, Geophys. Res. Lett., 23(9), 1017, doi:10.1029/
96GL00746.
Marisaldi, M., et al. (2010), Detection of terrestrial gamma ray flashes up
to 40 MeV by the AGILE satellite, J. Geophys. Res., 115, 1–12, doi:
10.1029/2009JA014502.
Marshall, T. C., and M. Stolzenburg (2001), Voltages inside and just
above thunderstorms, J. Geophys. Res., 106 (D5), 4757–4768, doi:
10.1029/2000JD900640.
Marshall, T. C., M. Stolzenburg, C. R. Maggio, L. M. Coleman, P. R.
Krehbiel, T. Hamlin, R. J. Thomas, and W. Rison (2005), Observed electric fields associated with lightning initiation, Geophys. Res. Lett., 32(3),
1–5, doi:10.1029/2004GL021802.
Østgaard, N., T. Gjesteland, J. Stadsnes, P. H. Connell, and B. Carlson
(2008), Production altitude and time delays of the terrestrial gamma
flashes: Revisiting the burst and transient source experiment spectra, J.
Geophys. Res., 113(A2), 1–14, doi:10.1029/2007JA012618.
Østgaard, N., T. Gjesteland, R. S. Hansen, A. B. Collier, and
B. Carlson (2012), The true fluence distribution of terrestrial gamma
flashes at satellite altitude, J. Geophys. Res., 117(A3), A03,327, doi:
10.1029/2011JA017365.
Shao, X.-M., T. Hamlin, and D. M. Smith (2010), A closer examination of
terrestrial gamma-ray flash-related lightning processes, J. Geophys. Res.,
115(April 2004), 1–8, doi:10.1029/2009JA014835.
Smith, D. M., L. I. Lopez, R. P. Lin, and C. P. Barrington-Leigh
(2005), Terrestrial gamma-ray flashes observed up to 20 MeV,
Science (New York, N.Y.), 307(5712), 1085–1088, doi:10.1126/science.
1107466.
Smith, D. M., et al. (2011a), The rarity of terrestrial gamma-ray flashes,
Geophys. Res. Lett., 38(8), 3–7, doi:10.1029/2011GL046875.
Smith, D. M., et al. (2011b), A terrestrial gamma-ray flash observed
from an aircraft, J. Geophys. Res., 116 (D20), D20,124, doi:10.1029/
2011JD016252.
Stolzenburg, M., T. C. Marshall, W. D. Rust, E. Bruning, D. R. Macgorman,
and T. Hamlin (2007), Electric field values observed near lightning flash initiations, Geophys. Res. Lett., 34, 1–7, doi:10.1029/2006
GL028777.
Tavani, M., et al. (2011), Terrestrial gamma-ray flashes as powerful particle accelerators, Phys. Rev. Lett., 106 (1), 1–5, doi:10.1103/
PhysRevLett.106.018501.
6. Conclusion
[31] In this paper we have shown how simulations of photon fluence at aircraft and balloon altitudes depend on the
initial conditions. For all observational altitudes the number of photons and the initial production altitude are the
two main parameters. When observations are made below
the initial production altitude of the TGF, other parameters
such as initial production altitude distribution, initial photon
angular distribution and amount of feedback also give large
differences. This means that one have to be careful when
making conclusions based on these type of simulations. The
comparisons to the non detection of ADELE together with
the results of Østgaard et al. [2012] support the possibility
that all discharges may produce TGFs.
[32] Acknowledgment. This study was supported by the Norwegian
Research Council under contract 208028/F50.
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Paper 3
6.3 An altitude and distance correction to the initial fluence distribution of TGFs
R. S. Nisi, N. Østgaard, T. Gjesteland, and A. Collier
Journal of Geophysical Research Space Physics, 2014
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Scientific results